Elliptic curves in class 12.1-c over 4.4.17428.1
Isogeny class 12.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-c1
| \( \bigl[a^{2} - 2\) , \( a^{2} + a - 3\) , \( a^{2} + a - 2\) , \( a^{3} + 2 a^{2} - 4 a - 3\) , \( a^{3} + 2 a^{2} - 3 a - 5\bigr] \)
|
| 12.1-c2
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 5 a - 3\) , \( a^{2} - 2\) , \( -9 a^{2} - 18 a\) , \( 4 a^{3} + 14 a^{2} + 10 a - 5\bigr] \)
|
| 12.1-c3
| \( \bigl[a\) , \( a^{3} + a^{2} - 4 a - 5\) , \( a^{3} - 3 a\) , \( -70 a^{3} - 38 a^{2} + 367 a + 278\) , \( -775 a^{3} - 407 a^{2} + 4026 a + 3044\bigr] \)
|
| 12.1-c4
| \( \bigl[a\) , \( a^{3} + a^{2} - 4 a - 5\) , \( 0\) , \( 448 a^{3} + 236 a^{2} - 2325 a - 1760\) , \( -12770 a^{3} - 6721 a^{2} + 66370 a + 50211\bigr] \)
|
| 12.1-c5
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -46 a^{3} + 81 a^{2} + 209 a - 346\) , \( -46 a^{3} + 81 a^{2} + 210 a - 346\bigr] \)
|
| 12.1-c6
| \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 184 a^{3} - 324 a^{2} - 846 a + 1379\) , \( -14 a^{3} + 15 a^{2} + 63 a - 67\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 8 & 4 & 8 \\
8 & 4 & 8 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)
