Elliptic curves in class 512.3-n over 4.4.2777.1
Isogeny class 512.3-n contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 512.3-n1
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 2\) , \( 0\) , \( -182 a^{3} + 237 a^{2} + 478 a - 468\) , \( -1492 a^{3} + 2365 a^{2} + 4197 a - 4226\bigr] \)
|
| 512.3-n2
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} + a - 4\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -309 a^{3} + 641 a^{2} + 775 a - 1350\) , \( -4864 a^{3} + 9157 a^{2} + 13057 a - 17838\bigr] \)
|
| 512.3-n3
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + 2 a^{2} + a - 4\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -19 a^{3} + 41 a^{2} + 45 a - 90\) , \( -70 a^{3} + 123 a^{2} + 195 a - 226\bigr] \)
|
| 512.3-n4
| \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a\) , \( a\) , \( -19 a^{3} + 47 a^{2} + 40 a - 95\) , \( -166 a^{3} + 234 a^{2} + 513 a - 322\bigr] \)
|
| 512.3-n5
| \( \bigl[a^{3} - 3 a\) , \( a^{3} - 5 a\) , \( a\) , \( a^{3} + 2 a^{2} + 5\) , \( 3 a^{3} + 3 a^{2} - 6 a - 4\bigr] \)
|
| 512.3-n6
| \( \bigl[a\) , \( -a - 1\) , \( a^{2} - a - 2\) , \( 2971 a^{3} - 138 a^{2} - 12996 a - 9100\) , \( -157120 a^{3} + 32554 a^{2} + 641687 a + 354554\bigr] \)
|
| 512.3-n7
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -665 a^{3} + 1278 a^{2} + 1788 a - 2528\) , \( -17480 a^{3} + 27918 a^{2} + 51201 a - 46226\bigr] \)
|
| 512.3-n8
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -15 a^{3} + 23 a^{2} + 53 a - 58\) , \( 21 a^{3} - 34 a^{2} - 85 a + 90\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 6 & 3 & 2 & 6 & 2 & 2 & 6 \\
6 & 1 & 2 & 12 & 4 & 3 & 12 & 4 \\
3 & 2 & 1 & 6 & 2 & 6 & 6 & 2 \\
2 & 12 & 6 & 1 & 3 & 4 & 4 & 12 \\
6 & 4 & 2 & 3 & 1 & 12 & 12 & 4 \\
2 & 3 & 6 & 4 & 12 & 1 & 4 & 12 \\
2 & 12 & 6 & 4 & 12 & 4 & 1 & 3 \\
6 & 4 & 2 & 12 & 4 & 12 & 3 & 1
\end{array}\right)\)
