| Locus | Group ID | Signature |
Generators | Comments and Favorite Equations | Additional files |
| 1 | (504,156) | (2,3,7) |
| \( (x_0, -x_1, -x_2, -x_3,x_4,x_5,-x_6)\) |
| \( (\frac{1}{2}(-x_1 + x_2 - x_3 + x_5),
\frac{1}{2}(x_0-x_1-x_2+x_4),
\frac{1}{2}(x_0,x_1,-x_3,x_6),
\frac{1}{2}(-x_0-x_2+x_5+x_6),
\frac{1}{2}(-x_1-x_4-x_5+x_6),
\frac{1}{2}(-x_0-x_3+x_4-x_5),
\frac{1}{2}(-x_2-x_2-x_4-x_6) \) |
|
| Macbeath's curve |
| \( x_0^2+x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2,\) |
| \( x_0^2+\zeta_{7} x_1^2+\zeta_{7}^2 x_2^2+\zeta_{7}^3 x_3^2+\zeta_{7}^4 x_4^2+\zeta_{7}^5 x_5^2+\zeta_{7}^6 x_6^2,\) |
| \(x_0^2+\zeta_{7}^{-1} x_1^2+\zeta_{7}^{-2} x_2^2+\zeta_{7}^{-3} x_3^2+\zeta_{7}^{-4} x_4^2+\zeta_{7}^{-5} x_5^2+\zeta_{7}^{-6} x_6^2,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_0 x_6-(\zeta_{7}^{-2}-\zeta_{7}^2) x_1 x_4+(\zeta_{7}-\zeta_{7}^{-1}) x_3 x_5,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_1 x_0-(\zeta_{7}^{-2}-\zeta_{7}^2) x_2 x_5+(\zeta_{7}-\zeta_{7}^{-1}) x_4 x_6,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_2 x_1-(\zeta_{7}^{-2}-\zeta_{7}^2) x_3 x_6+(\zeta_{7}-\zeta_{7}^{-1}) x_5 x_0,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_3 x_2-(\zeta_{7}^{-2}-\zeta_{7}^2) x_4 x_0+(\zeta_{7}-\zeta_{7}^{-1}) x_6 x_1,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_4 x_3-(\zeta_{7}^{-2}-\zeta_{7}^2) x_5 x_1+(\zeta_{7}-\zeta_{7}^{-1}) x_0 x_2,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_5 x_4-(\zeta_{7}^{-2}-\zeta_{7}^2) x_6 x_2+(\zeta_{7}-\zeta_{7}^{-1}) x_1 x_3,\) |
| \((\zeta_{7}^{-3}-\zeta_{7}^3) x_6 x_5-(\zeta_{7}^{-2}-\zeta_{7}^2) x_0 x_3+(\zeta_{7}-\zeta_{7}^{-1}) x_2 x_4\) |
| Genus-7-504-156.htm |
| 2 | (144,127) | (2,3,12) |
| \( (-x_0, (-\zeta_{12}^3 + \zeta_{12})x_1 - \zeta_{12}x_2, -\zeta_{12}x_1 + (\zeta_{12}^3 - \zeta_{12})x_2 ,
(-\zeta_{12}^2 + 1)x_4 , \zeta_{12}^2x_3, \zeta_{12}^2x_3 + \zeta_{12}^2x_6, (\zeta_{12}^2 - 1)x_4 +
(-\zeta_{12}^2 + 1)x_5 \) |
| \( ( (\zeta_{12}^2 - 1)x_0, -x_1 + \zeta_{12}^2x_2 , (\zeta_{12}^2 - 1)x_1, (\zeta_{12}^2 - 1)x_3 ,
(\zeta_{12}^2 - 1)x_4 + (-\zeta_{12}^2 + 1)x_5 , -\zeta_{12}^2x_5 ,
x_3 + x_6 ) \) |
|
| \(x_0^2 + x_3 x_4 - \zeta_{6} x_3 x_5 - \zeta_{6} x_5 x_6,\) |
| \(2 i x_1^2 + x_3 x_4 + \zeta_{6} x_3 x_5 + 2 x_4 x_6 - \zeta_{6} x_5 x_6,\) |
| \(2 i x_1 x_2 +(-2 \zeta_{12}^2 + 1) x_3 x_4 + \zeta_{6} x_3 x_5 - 2 \zeta{6} x_4 x_6 + \zeta_{6} x_5 x_6,\) |
| \(2 i x_2^2 -x_3 x_4 +(-\zeta_{6} + 2) x_3 x_5 + (2 \zeta_{6} - 2) x_4 x_6 +(-\zeta_{6} + 2) x_5 x_6,\) |
| \(x_1 x_3 - \zeta_{6} x_2 x_6 + \zeta_{12} x_4^2 + (i - 2 \zeta_{12}) x_4 x_5 + \zeta_{12} x_5^2,\) |
| \(x_1 x_4 +(-\zeta_{6} + 1) x_2 x_5 -x_3 x_6 - x_6^2,\) |
| \(x_1 x_5 - x_2 x_5 + x_3^2 +(-\zeta_{6} + 2) x_3 x_6,\) |
| \(x_1 x_6 + x_2 x_6 -\zeta_{12} x_4^2 + \zeta_{12} x_4 x_5 - \zeta_{12} x_5^2,\) |
| \(x_2 x_3 - \zeta_{6} x_2 x_6 + \zeta_{12} x_4^2,\) |
| \(x_2 x_4 +(-\zeta_{6} - 1) x_2 x_5 + \zeta_{6} x_3^2 + 2
\zeta_{6} x_3 x_6 + \zeta_{6} x_6^2\) |
| Genus-7-144-127.htm |
| 3 | (64,41) | (2,4,16) |
| \( (-x_0,x_2,x_1,x_4,x_3,x_6,x_6)\) |
| \( (\zeta_{8}^2x_0, -\zeta_{8} x_2,
-\zeta_{8}^3x_1,x_6,-\zeta_{8}x_5,-\zeta_{8}^3 x_4,x_3) \) |
|
| \( x_0^2+x_1 x_2 \) |
| \(x_3 x_4-\zeta_{16}^2 x_5 x_6\) |
| \(x_1^2+x_3 x_6+ \zeta_{16}^4 x_4 x_5\) |
| \(x_2^2+\zeta_{16}^4 x_3 x_6+x_4 x_5 \) |
| \(x_0 x_1+\zeta_{16}^{-1} x_3^2+\zeta_{16}^6 x_5^2 \) |
| \(x_0 x_2-\zeta_{16}^{-1} x_4^2-\zeta_{16}^5 x_6^2\) |
| \(x_0 x_3-\zeta_{16} x_2 x_6 \) |
| \(x_0 x_4-\zeta_{16} x_1 x_5 \) |
| \(x_0 x_5+\zeta_{16}^{-1} x_2 x_4 \) |
| \(x_0 x_6-\zeta_{16}^{-1} x_1 x_3\) |
| Genus-7-64-41.htm |
| 4 | (64,38) | (2,4,16) |
| \( (2, 7)(3, 12)(5, 13)(8, 10)(9, 19)(11, 21)(14, 22)(15, 27)(16, 26)(18, 20)(23, 24)(25, 31)(28, 32)(29, 30)\) |
| \( (1, 2, 4, 9)(3, 7, 14, 19)(5, 18, 16, 29)(6, 11, 17, 25)(8, 22, 23, 12)(10, 26, 24, 13)(15, 21, 28, 31)(20, 32, 30, 27) \) |
| Hyperelliptic, \( y^2=x^{16}-1\) | Genus-7-64-38.txt |
| 5 | (56,4) | (2,4,28) |
| \( (1, 16)(2, 20)(3, 22)(4, 9)(5, 25)(6, 12)(7, 14)(8, 23)(10, 18)(11, 26)(13, 27)(17, 28)\) |
| \( (1, 12, 3, 18)(2, 14, 5, 9)(4, 6, 7, 10)(8, 20, 13, 25)(11, 22, 17, 16)(15, 26, 21, 28)(19, 27, 24, 23)\) |
| Hyperelliptic, \( y^2 = x^{15}-x\) | Genus-7-56-4.txt |
| 6 | (54,6) |
(2,6,9) |
| \( (-x_0, (\zeta_{18}^5-\zeta_{18}^2)x_6,\zeta_{18}^2 x_4, -\zeta_{18}^5 x_5, (-\zeta_{18}^{4}+\zeta_{18})x_2,\zeta_{18}^4 x_3, -\zeta_{18}x_1) \) |
| \( (\zeta_{6}x_0, (\zeta_{6}-1)x_5, (\zeta_{6}-1)x_6,(\zeta_{6}-1)x_4,-\zeta_{6}x_1,-\zeta_{6}x_2,-\zeta_{6}x_3) \) |
|
| \( x_1 x_6+x_2 x_4+x_3 x_5 \) |
| \( x_0^2-x_1 x_6+\zeta_{6} x_2 x_4-(\zeta_{6}-1) x_3 x_5\) |
| \( x_1 x_4+(\zeta_{6}-1) x_2 x_5-\zeta_{6} x_3 x_6\) |
| \( x_1 x_5+(\zeta_{6}-1) x_2 x_6-\zeta_{6} x_3 x_4\) |
| \( x_0 x_1-x_4 x_6-\zeta_{6} x_5^2\) |
| \( x_0 x_2-(\zeta_{6}-1) x_4 x_5+x_6^2\) |
| \( x_0 x_3+(\zeta_{6}-1) x_4^2+\zeta_{6} x_5 x_6\) |
| \( x_0 x_4-x_1^2+(\zeta_{6}-1) x_2 x_3\) |
| \( x_0 x_5-\zeta_{6} x_1 x_3-(\zeta_{6}-1) x_2^2\) |
| \( x_0 x_6+x_1 x_2+\zeta_{6} x_3^2\) |
|
Genus-7-54-6ab.htm |
| 7 | (54,6) | (2,6,9) | |
Complex conjugate
of the previous entry | See the discussion at the end of
Genus-7-54-6ab.htm |
| 8 | (54,3) | (2,6,9) |
| \((x_1,x_0,-x_6,-x_5,-x_4,-x_3,-x_2)\) |
| \( (\zeta_9 x_1, \zeta_9^2 x_0,-\zeta_9 x_6, -\zeta_9^2 x_5, -\zeta_9^3 x_4, -\zeta_9^4 x_3, -\zeta_9^5 x_2) \) |
|
| Cyclic trigonal \( y^3 = x^9-1\) |
| \( 2\times 2\) minors of
\( \left[ \begin{array}{rrrrr} x_0 & x_2 & x_3 & x_4 & x_5 \\ x_1 & x_3 & x_4 & x_5 & x_6 \end{array} \right]\), and |
| \( x_0^3-x_6^2+x_2^3 \) |
| \( x_0^2 x_1-x_6^2 x_4+x_2^2 x_3, \) |
| \( x_0 x_1^2-x_6^2 x_5+x_2^2 x_4, \) |
| \( x_1^3-x_6^3+x_2^2 x_5 \) |
| Genus-7-54-3.htm |
| 9 | (48,32) | (3,4,6) |
| \( ( (\zeta_{6}-1)x_0, (-\zeta_{6}+1)x_2,-\zeta_6 x_1-x_2, -x_3+\zeta_6 x_4, (\zeta_6-1)x_3, (\zeta_6-1)x_5-\zeta_6 x_6, x_6) \) |
| \( (-x_0,x_2,-x_1,-x_4,x_3,(\zeta_6-1)x_5-\zeta_6 x_6, -\zeta_6 x_5 +(-\zeta_6 + 1)x_6\) |
|
| \( x_0^2+x_3 x_5+\zeta_{6} x_3 x_6+(-\zeta_{6}+1) x_4 x_6 \) |
| \( x_1 x_3+x_1 x_5+((2/3) \zeta_{6}-1/3) x_1 x_6-x_2 x_4+(-(2/3) \zeta_{6}+1/3) x_2 x_5+((2/3) \zeta_{6}-1/3) x_2 x_6 \) |
| \( x_1 x_4+(-(1/3) \zeta_{6}+1/6) x_1 x_5+((1/3) \zeta_{6}-1/6) x_1 x_6-(1/2) x_2 x_5+(1/2) x_2 x_6 \) |
| \( (-\zeta_{6}+1/2) x_1 x_5+(1/2) x_1 x_6+x_2 x_3-(1/2) x_2 x_5+(-(1/3) \zeta_{6}+1/6) x_2 x_6 \) |
| \( x_1^2+x_3 x_5-x_3 x_6+(-(2/3) \zeta_{6}+1/3) x_4 x_5+((2/3) \zeta_{6}-1/3) x_4 x_6-(2/3) x_5^2+(-(2/3) \zeta_{6}+2/3) x_5 x_6+(2/3) \zeta_{6} x_6^2 \) |
| \( x_1 x_2+(-(2/3) \zeta_{6}+1/3) x_3 x_5+((2/3) \zeta_{6}-1/3) x_3 x_6-x_4 x_5+(-(2/3) \zeta_{6}+1/3) x_4 x_6+((2/3) \zeta_{6}-1/3) x_5^2-(2/3) \zeta_{6} x_5 x_6+(1/3) x_6^2 \) |
| \( x_2^2-x_3 x_5+(-(2/3) \zeta_{6}+1/3) x_3 x_6+(2 \zeta_{6}-1) x_4 x_5-x_4 x_6+(-(2/3) \zeta_{6}-2/3) x_5 x_6+(-(2/3) \zeta_{6}+2/3) x_6^2 \) |
| \( -(1/2) x_3 x_5+(1/2) x_3 x_6+x_4^2+((1/3) \zeta_{6}-1/6) x_4 x_5+(-(1/3) \zeta_{6}+1/6) x_4 x_6-(1/3) x_5^2+(-(1/3) \zeta_{6}+1/3) x_5 x_6+(1/3) \zeta_{6} x_6^2 \) |
| \( -x_3 x_4+((1/3) \zeta_{6}-1/6) x_3 x_5+(-(1/3) \zeta_{6}+1/6) x_3 x_6+(1/2) x_4 x_5+((1/3) \zeta_{6}-1/6) x_4 x_6+((1/3) \zeta_{6}-1/6) x_5^2-(1/3) \zeta_{6} x_5 x_6+(1/6) x_6^2 \) |
| \( x_3^2+(1/2) x_3 x_5+((1/3) \zeta_{6}-1/6) x_3 x_6+(-\zeta_{6}+1/2) x_4 x_5+(1/2) x_4 x_6+(-(1/3) \zeta_{6}-1/3) x_5 x_6+(-(1/3) \zeta_{6}+1/3) x_6^2 \) |
| Genus-7-48-32.htm |
| 10 | (42,4) | (2,6,21) |
| \(
(\zeta_7 x_1,\zeta_7^6 x_0,-\zeta_7^4 x_6,-\zeta_7^2x_5,-x_4,-\zeta_7^5 x_3,-\zeta_7^3 x_2)\) |
| \( (\zeta_{21}^{-2} x_1, \zeta_{21}^{-5} x_0,-\zeta_{21}^{-1} x_6, -\zeta_{21}^{-4} x_5, (\zeta_3+1) x_4, -\zeta_{21}^{11} x_3, -\zeta_{21}^8 x_2 )\) |
|
| Cyclic trigonal \( y^3 = x^8-x \) |
| \(2\times 2\) minors of
\( \left[ \begin{array}{rrrrr} x_0 & x_2 & x_3 & x_4 & x_5 \\ x_1 & x_3 & x_4 & x_5 & x_6 \end{array} \right]\), and |
| \(x_0^3-x_6^2 x_2+x_2^2 x_3\) |
| \( x_0^2 x_1-x_6^2 x_3+x_2^2 x_4,\) |
| \( x_0 x_1^2-x_6^2 x_4+x_2^2 x_5,\) |
| \( x_1^3-x_6^2 x_5+x_2^2 x_6\) |
| Genus-7-42-4.htm |
| 11 | (32,11) | (4,4,8) |
| \( (-x_0,-x_2,x_1,-ix_4,-ix_3,ix_6,ix_5)\) |
| \( (ix_0,x_1,ix_2,-x_3,-ix_4,-x_5,ix_6)\) |
|
| \( x_3 x_5+x_4 x_6, \) |
| \(x_0^2+x_1 x_5+\zeta_8^2 x_2 x_6,\) |
| \(x_1 x_4+\zeta_8^2 x_2 x_3+x_5 x_6,\) |
| \(x_1 x_2+x_3 x_4,\) |
| \(x_1 x_6+\zeta_8^3 x_4 x_5,\) |
| \(x_2 x_5+\zeta_8 x_3 x_6,\) |
| \(x_1^2-\zeta_8^2 x_3^2-\zeta_8^3 x_5^2,\) |
| \(x_2^2+\zeta_8^2 x_4^2+\zeta_8^3 x_6^2,\) |
| \(-\zeta_8^2 x_2 x_4+\zeta_8^3 x_3^2,\) |
| \(x_1 x_3-\zeta_8^3 x_4^2\) |
| Genus-7-32-11.htm |
| 12 | (32,10) |
(4,4,8) |
| \( (-x_0,-x_2,x_1,-\zeta_{16}^2 x_4,-\zeta_{16}^6 x_3, -\zeta_{16}^6 x_6, -\zeta_{16}^2 x_5)\) |
| \( (\zeta_{16}^4 x_0, -\zeta_{16}^6 x_2,-\zeta_{16}^2 x_1, -\zeta_{16}^4 x_4, \zeta_{16}^4 x_3, -\zeta_{16}^4 x_6, -\zeta_{16}^4 x_5) \) |
|
| \( x_1 x_6+\zeta_{16}^6 x_2 x_5+x_3 x_4, \) |
| \(x_1 x_2+x_5 x_6,\) |
| \(x_0^2+x_1 x_6-\zeta_{16}^6 x_2 x_5,\) |
| \(x_3 x_6-\zeta_{16}^4 x_4 x_5,\) |
| \(x_1^2-\zeta_{16}^7 x_4^2-\zeta_{16}^6 x_5^2,\) |
| \(x_2^2+\zeta_{16}^3 x_3^2-\zeta_{16}^10 x_6^2,\) |
| \(-\zeta_{16}^2 x_2 x_6+(\zeta_{16}^{16}+\zeta_{16}^8) x_4^2-\zeta_{16}^7 x_5^2,\) |
| \(x_1 x_5+(-\zeta_{16}^{12}-\zeta_{16}^4) x_3^2-\zeta_{16}^{11} x_6^2,\) |
| \(x_1 x_3+\zeta_{16}^7 x_4 x_6,\) |
| \(x_2 x_4+\zeta_{16} x_3 x_5\) |
| Genus-7-32-10.htm |
| 13 | (30,4) | (2,15,30) |
| \( (1, 2)(3, 7)(4, 8)(5, 9)(6, 10)(11, 17)(12, 18)(13, 19)(14, 20)(15, 21)(16,
22)(23, 27)(24, 28)(25, 29)(26, 30)\) |
| \( (1, 26, 11, 6, 25, 3, 16, 14, 12, 13, 5, 24, 4, 15, 23)(2, 30, 17, 10, 29, 7,
22, 20, 18, 19, 9, 28, 8, 21, 27)\) |
| Hyperelliptic, \(y^2 = x^{15}-1\) | Genus-7-30-4.txt |
| Locus | Group ID | Signature |
Generators | Comments and Favorite Equations | Additional files |
| 14 | (48,48) | (2,2,2,4) |
| \( (-x_0,x_2+x_3,-x_2,x_1+x_2,-x_4+x_5+x_6,x_6,x_5) \) |
| \( (-x_0, x_1+x_2,-x_2,x_2+x_3,-x_6,x_4-x_5-x_6,-x_4) \) |
| \( (-x_0,x_1,-x_1-x_2,-x_3,-x_4,x_5,-x_5-x_6) \) |
|
| \( x_0^2 + x_4^2 + x_4 x_6 + x_5^2 - x_5 x_6 + x_6^2, \) |
| \( x_1^2 - x_1 x_2 + x_2^2 - x_2 x_3 + x_3^2+x_4^2 + x_4 x_6 + x_5^2 - x_5 x_6 + x_6^2,\) |
| \( (c_{13}^2+6) (x_1^2 - 2 x_1 x_3 - x_2^2 + x_3^2)+c_{13}^2 (x_4^2 - 2 x_4 x_5 + 2 x_4 x_6 + x_5^2 - 2 x_5 x_6),\) |
| \( (c_{13}^2+6) (x_1 x_2 - 2 x_1 x_3 - 1/2 x_2^2 + x_2 x_3)+ c_{13}^2 (-2 x_4 x_5 + x_4 x_6 - x_5 x_6 + 1/2 x_6^2),\) |
| \( c_{13} (x_0 x_4 + x_0 x_5 + x_0 x_6)+((c_{13}^2+6)/2) (x_1^2 - x_3^2)+(c_{13}^2/2) (x_4^2 + 2 x_4 x_6 - x_5^2 + x_6^2),\) |
| \( c_{13} (x_0 x_4 + x_0 x_5)+((c_{13}^2+6)/2) (x_1 x_2 - x_2 x_3)+(c_{13}^2/2) (x_4 x_6 - x_5 x_6 + x_6^2),\) |
| \( c_{13} (2 x_0 x_4 + x_0 x_6)+((c_{13}^2+6)/2) (x_2^2 - 2 x_2 x_3)+(c_{13}^2/2) (2 x_4 x_6 + x_6^2),\) |
| \( x_0 x_1 + x_0 x_3+c_{13} (x_1 x_5 - x_3 x_4 - x_3 x_6),\) |
| \( 2 x_0 x_1 - x_0 x_2+c_{13} (x_1 x_6 + x_2 x_5 - x_2 x_6),\) |
| \( x_0 x_2 - 2 x_0 x_3+c_{13} (x_2 x_4 + x_3 x_6)\) |
| Genus-7-48-48.htm |
| 15 | (48,41) | (2,2,2,4) |
| \( ( -x_0,-x_1,x_2,ix_5,-ix_6,-ix_3,ix_4)\) |
| \( (-x_0,ix_2,-ix_1,(\zeta_{12}^2-1)x_6,-(\zeta_{12}^2-1)x_5,\zeta_{12}^2x_4,-\zeta_{12}^2x_3)\) |
| \( (-x_0,x_2,x_1,\zeta_{12}x_6,\zeta_{12}x_5,(-\zeta_{12}^3+\zeta_{12})x_4,(-\zeta_{12}^3+\zeta_{12})x_3)\) | |
|
|
| \( x_0^2+ x_3 x_6 - x_4 x_5, \) |
| \( x_1^2 - x_2^2 + x_3 x_5 - x_4 x_6,\) |
| \( (c_9^2-2 i) x_1 x_2 + i (x_3 x_6 + x_4 x_5),\) |
| \( (c_9^2-2 i) (x_1^2 + x_2^2) - c_9^2 (x_3 x_5 + x_4 x_6),\) |
| \( c_9 (x_1 x_3 + x_2 x_4)-i x_5^2 - i x_6^2,\) |
| \( c_9 (x_1 x_5 + x_2 x_6) +x_3^2 + x_4^2,\) |
| \( x_1 x_4 + x_2 x_3+c_9 x_5 x_6,\) |
| \( x_1 x_6 + x_2 x_5+i c_9 (x_3 x_4),\) |
| \( (c_9^2-2 i) (x_1 x_3 - x_2 x_4) +c_9 (i x_5^2 - i x_6^2),\) |
| \( (c_9^2-2 i) (x_1 x_5 - x_2 x_6) -c_9 (x_3^2 - x_4^2)\) |
| Genus-7-48-41.htm |
| 16 | (48,38) | (2,2,2,4) |
| \( (-x_0,x_1,-x_2,-\zeta_6 x_5,\zeta_6 x_6,(\zeta_6-1) x_3, (-\zeta_6+1)x_4)\) |
| \( (-x_0,-x_1,-x_2,-x_5,-x_6,-x_3,-x_4)\) |
| \( (-x_0,-x_2,-x_1,-x_6,-x_5,-x_4,-x_3)\) |
|
| \( x_0^2+ x_3 x_5 + x_4 x_6, \) |
| \( (2 c_{10}+1) (x_1^2 + x_2^2) -c_{10} (x_3 x_5 + x_4 x_6),\) |
| \( (2 c_{10}+1) x_1 x_2 -c_{10}^2 (x_3 x_6 + x_4 x_5),\) |
| \( x_1^2 - x_2^2 + c_{10} (x_3 x_5 - x_4 x_6),\) |
| \( (2 c_{10}+1) (x_1 x_3 - x_2 x_4)-c_{10} (x_5^2 - x_6^2),\) |
| \( (2 c_{10}+1) (x_1 x_5 - x_2 x_6) -c_{10} (x_3^2 - x_4^2),\) |
| \( x_1 x_3 + x_2 x_4 + c_{10} (x_5^2 + x_6^2),\) |
| \( x_1 x_5 + x_2 x_6 + c_{10} (x_3^2 + x_4^2),\) |
| \( x_1 x_4 + x_2 x_3 +x_5 x_6,\) |
| \( x_1 x_6 + x_2 x_5 + x_3 x_4\) |
| Genus-7-48-38.htm |
| 17 | (36,10) | (2,2,2,6) |
| \( (-x_0,x_2,x_1,-x_3-x_4,x_4,x_6,x_5)\) |
| \( (-x_0,x_1-x_2,-x_2,x_5,x_3+x_4-x_6,x_3,x_3+x_5-x_6)\) |
| \( (-x_0,-x_1,-x_2,x_5,-x_3-x_4-x_5+x_6,x_3,x_6)\) |
|
| \( x_0^2+c_3 (x_3^2 - x_3 x_4 - x_3 x_5 + 1/2 x_3 x_6 + x_4^2 + 1/2 x_4 x_5 + 1/2 x_4 x_6 + x_5^2 + 1/2 x_5 x_6 + x_6^2),\) |
| \( x_1^2 + x_1 x_2 + x_2^2+(c_3+6) (x_3^2 - x_3 x_4 - x_3 x_5 + 1/2 x_3 x_6 + x_4^2 + 1/2 x_4 x_5 + 1/2 x_4 x_6 + x_5^2 + 1/2 x_5 x_6 + x_6^2),\) |
| \( x_0 x_1 -x_1^2 -2 x_1 x_2 -3 (-2 x_3 x_4 - x_3 x_6 + x_4^2 + x_4 x_5 - x_5 x_6 - x_6^2),\) |
| \( x_0 x_2 +2 x_1 x_2 + x_2^2-3 (x_3^2 - x_3 x_5 + x_3 x_6 - x_4^2 - x_4 x_6 + x_5^2 + x_5 x_6),\) |
| \( x_1 x_3 + x_1 x_4 + 2 x_1 x_6 + 2 x_2 x_3 - x_2 x_4 + x_2 x_6 + x_3^2 - x_3 x_4 + 2 x_3 x_5 + 2 x_3 x_6 + x_4^2 - x_4 x_5 + 2 x_4 x_6 - 2 x_5^2 - x_5 x_6 + x_6^2,\) |
| \( x_1 x_5 + 2 x_1 x_6 + 2 x_2 x_5 + x_2 x_6+ 2 x_3^2 -2 x_3 x_4 - 2 x_3 x_5 + x_3 x_6 + 2 x_4^2 + x_4 x_5 + x_4 x_6 - x_5^2- 2 x_5 x_6 - x_6^2,\) |
| \( x_0 x_3 + x_1 x_4 - x_1 x_5 - x_2 x_3 + x_2 x_4 - x_2 x_6 + x_3^2 + 2 x_3 x_4 + 2 x_3 x_5 + 2 x_3 x_6 - 2 x_4^2 - 4 x_4 x_5 - 4 x_4 x_6 - 2 x_5^2 - 4 x_5 x_6 - 2 x_6^2,\) |
| \( x_0 x_4 + x_1 x_3 - x_1 x_5 + x_2 x_4 + 2 x_3 x_4 - 2 x_3 x_6 - x_4^2 - 4 x_4 x_5 - 2 x_5 x_6 - 2 x_6^2,\) |
| \( x_0 x_5 -x_1 x_5 - x_2 x_5 - x_2 x_6 + 2 x_3^2 - 2 x_3 x_5 + 2 x_3 x_6 - 2 x_4^2 - 2 x_4 x_6 - x_5^2 - 4 x_5 x_6,\) |
| \( x_0 x_6 + x_1 x_5 + x_1 x_6 + x_2 x_6 + -4 x_3 x_4 - 2 x_3 x_6 + 2 x_4^2 + 2 x_4 x_5 + 4 x_5 x_6 + x_6^2\) |
| Genus-7-36-10.htm |
| 18 | (32,43) | (2,2,2,8) |
| \( (-x_0,-x_1,-x_2,-x_3,-x_4,x_5,x_6)\) |
| \( (-x_0,-x_2,-x_1,-ix_6,-x_5,-x_4,ix_3)\) |
| \( (-x_0,-x_1,x_2,-ix_4,ix_3,-ix_6,ix_5)\) |
|
| \( x_0^2+ 2 x_3 x_4 - 2 i x_5 x_6,\) |
| \( x_1^2 + x_2^2-2 x_3 x_4 +2 i x_5 x_6,\) |
| \( x_3 x_6 - x_4 x_5,\) |
| \( x_1^2 - x_2^2+c_8 (x_3 x_4 + i x_5 x_6),\) |
| \( x_0 x_1+x_3^2-x_4^2-i x_5^2+i x_6^2,\) |
| \( x_0 x_2-x_5^2-x_6^2-i x_3^2-i x_4^2,\) |
| \( x_0 x_3-x_1 x_4-i x_2 x_4,\) |
| \( x_0 x_4+x_1 x_3-i x_2 x_3,\) |
| \( x_0 x_5-i x_2 x_6-x_1 x_6,\) |
| \( x_0 x_6-i x_2 x_5+x_1 x_5 \) |
| Genus-7-32-43.htm |
| 19 | (32,42) | (2,2,2,8) |
| \( (-x_0,-x_2,-x_1,\zeta_8 x_4,-\zeta_8^3 x_3,\zeta_8^3 x_6,-\zeta_8 x_5)\) |
| \( (-x_0,x_1,-x_2,-ix_4,ix_3,-x_6,-x_5)\) |
| \( (-x_0,-x_1,-x_2,-x_3,x_4,x_5,-x_6)\) |
|
| \( x_0^2+x_1^2 + x_2^2, \) |
| \( x_1 x_2+x_3 x_6 + i x_4 x_5,\) |
| \( x_3 x_4+x_5 x_6,\) |
| \( x_1^2 - x_2^2+c_8 (x_3 x_6 - i x_4 x_5),\) |
| \( x_0 x_1+((1/2) \zeta_8^{-1} c_8 -\zeta_8) (x_3^2 + x_4^2)+((1/2) \zeta_8 c_8 -\zeta_8^{-1}) (x_5^2 -x_6^2),\) |
| \( x_0 x_2+((1/2) \zeta_8^{-1} c_8 -\zeta_8) (i x_3^2 - i x_4^2)+((1/2) \zeta_8 c_8 -\zeta_8^{-1}) (i x_5^2 + i x_6^2),\) |
| \( x_0 x_5+\zeta_8^3 (i x_1 x_4 - x_2 x_4),\) |
| \( x_0 x_6+\zeta_8^3 (x_1 x_3 -i x_2 x_3),\) |
| \( x_0 x_3-\zeta_8^3 (i x_1 x_6 - x_2 x_6),\) |
| \( x_0 x_4-\zeta_8^3 (x_1 x_5 -i x_2 x_5) \) |
| Genus-7-32-42.htm |
| 20 | (32,39) | (2,2,2,8) |
| \( (1, 10)(2, 14)(3, 5)(4, 15)(6, 16)(7, 8)(9, 11)(12, 13)\) |
| \( (1, 4)(2, 8)(3, 9)(5, 11)(7, 14)(10, 15)\) |
| \((1, 6)(2, 4)(3, 13)(5, 12)(7, 9)(8, 11)(10, 16)(14, 15)\) |
| Hyperelliptic | Genus-7-32-39.htm |
| 21 | (28,3) | (2,2,2,14) |
| \( (1, 2)(3, 4)(5, 7)(6, 8)(9, 11)(10, 12)(13, 14) \) |
| \( (1, 12)(2, 10)(3, 8)(4, 6)(5, 14)(7, 13)(9, 11) \) |
| \( (1, 4)(2, 3)(5, 8)(6, 7)(9, 12)(10, 11)(13, 14) \) |
| Hyperelliptic | Genus-7-28-3.htm |
