Elliptic curves in class 12.1-c over 4.4.13068.1
Isogeny class 12.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-c1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{2} - 3 a - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 22 a^{3} - 19 a^{2} - 119 a - 80\) , \( 112 a^{3} - 154 a^{2} - 502 a - 204\bigr] \)
|
| 12.1-c2
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{2} - a - 3\) , \( -306 a^{3} + 871 a^{2} + 246 a - 183\) , \( 154713 a^{3} - 436911 a^{2} - 131338 a + 84814\bigr] \)
|
| 12.1-c3
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{2} - a - 3\) , \( 1034 a^{3} - 2914 a^{2} - 889 a + 552\) , \( 45861 a^{3} - 129507 a^{2} - 38946 a + 25134\bigr] \)
|
| 12.1-c4
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 1\) , \( -a^{2} + 3 a + 4\) , \( a + 1\) , \( 70 a^{3} - 191 a^{2} - 89 a + 32\) , \( 708 a^{3} - 1980 a^{2} - 702 a + 341\bigr] \)
|
| 12.1-c5
| \( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 11 a\) , \( a^{3} - a^{2} - 6 a\) , \( -224 a^{3} + 349 a^{2} + 1144 a - 432\) , \( 2338 a^{3} - 3603 a^{2} - 12042 a + 4211\bigr] \)
|
| 12.1-c6
| \( \bigl[a\) , \( -a^{2} + 3 a + 4\) , \( a^{3} - a^{2} - 6 a\) , \( -41 a^{3} + 75 a^{2} + 198 a - 131\) , \( -263 a^{3} + 463 a^{2} + 1290 a - 786\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 2\)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 2 & 4 & 2 \\
4 & 1 & 2 & 8 & 4 & 8 \\
2 & 2 & 1 & 4 & 2 & 4 \\
2 & 8 & 4 & 1 & 8 & 4 \\
4 & 4 & 2 & 8 & 1 & 8 \\
2 & 8 & 4 & 4 & 8 & 1
\end{array}\right)\)
