Elliptic curves in class 4.1-c over 4.4.13068.1
Isogeny class 4.1-c contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 4.1-c1
| \( \bigl[-a^{3} + 2 a^{2} + 5 a - 2\) , \( -2 a^{3} + 3 a^{2} + 9 a - 2\) , \( 0\) , \( 14 a^{3} - 34 a^{2} - 26 a - 1\) , \( -28 a^{3} + 89 a^{2} - a - 32\bigr] \)
|
| 4.1-c2
| \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( 2 a^{3} - 3 a^{2} - 9 a + 1\) , \( a^{2} - 2 a - 3\) , \( 4 a^{3} - 6 a^{2} - 18 a\) , \( -4 a^{3} + 12 a^{2} + 2 a - 4\bigr] \)
|
| 4.1-c3
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( -3 a^{3} + 4 a^{2} + 15 a + 3\) , \( -2 a^{3} + 2 a^{2} + 11 a + 4\bigr] \)
|
| 4.1-c4
| \( \bigl[a^{3} - a^{2} - 6 a\) , \( 0\) , \( a^{3} - a^{2} - 6 a\) , \( 10 a^{3} - 28 a^{2} - 8 a + 3\) , \( -5 a^{3} + 14 a^{2} + 5 a - 4\bigr] \)
|
| 4.1-c5
| \( \bigl[a + 1\) , \( -a\) , \( a^{3} - a^{2} - 6 a\) , \( 17 a^{3} - 27 a^{2} - 165 a - 106\) , \( -260 a^{3} + 42 a^{2} + 1171 a + 418\bigr] \)
|
| 4.1-c6
| \( \bigl[a + 1\) , \( -a\) , \( a^{3} - a^{2} - 6 a\) , \( -8 a^{3} + 13 a^{2} + 35 a - 26\) , \( -27 a^{3} + 38 a^{2} + 133 a - 48\bigr] \)
|
| 4.1-c7
| \( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 46 a^{2} - 109 a - 37\) , \( -254 a^{3} - 346 a^{2} + 358 a + 262\bigr] \)
|
| 4.1-c8
| \( \bigl[a + 1\) , \( 2 a^{3} - 3 a^{2} - 10 a + 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 6 a^{2} - 14 a + 3\) , \( -2 a^{3} - 4 a^{2} + 3 a + 6\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 1\)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 4 & 2 & 12 & 6 \\
3 & 1 & 12 & 4 & 12 & 6 & 4 & 2 \\
4 & 12 & 1 & 3 & 4 & 2 & 12 & 6 \\
12 & 4 & 3 & 1 & 12 & 6 & 4 & 2 \\
4 & 12 & 4 & 12 & 1 & 2 & 3 & 6 \\
2 & 6 & 2 & 6 & 2 & 1 & 6 & 3 \\
12 & 4 & 12 & 4 & 3 & 6 & 1 & 2 \\
6 & 2 & 6 & 2 & 6 & 3 & 2 & 1
\end{array}\right)\)
