Elliptic curves in class 115.1-A over 3.1.23.1
Isogeny class 115.1-A contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 115.1-A1
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \)
|
| 115.1-A2
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( 4 a^{2} - 7 a + 2\bigr] \)
|
| 115.1-A3
| \( \bigl[a^{2}\) , \( -a^{2} - 1\) , \( 0\) , \( 6 a^{2} + 15 a + 10\) , \( 29 a^{2} - 28 a - 39\bigr] \)
|
| 115.1-A4
| \( \bigl[a^{2} + 1\) , \( a + 1\) , \( a + 1\) , \( 80 a^{2} + 75 a + 10\) , \( -199 a^{2} + 536 a + 518\bigr] \)
|
| 115.1-A5
| \( \bigl[a + 1\) , \( a^{2} + a\) , \( 0\) , \( -1347 a^{2} + 2368 a - 1788\) , \( 34299 a^{2} - 60188 a + 45434\bigr] \)
|
| 115.1-A6
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -15 a^{2} + 6 a - 10\) , \( -31 a^{2} + 6 a - 8\bigr] \)
|
| 115.1-A7
| \( \bigl[1\) , \( -a^{2} + 1\) , \( a + 1\) , \( -341 a^{2} + 550 a - 401\) , \( -3926 a^{2} + 6899 a - 5146\bigr] \)
|
| 115.1-A8
| \( \bigl[a\) , \( a + 1\) , \( a\) , \( -130 a^{2} + 61 a - 30\) , \( 520 a^{2} - 496 a - 4\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 4 & 3 & 2 & 6 & 4 & 12 \\
12 & 1 & 3 & 4 & 6 & 2 & 12 & 4 \\
4 & 3 & 1 & 12 & 2 & 6 & 4 & 12 \\
3 & 4 & 12 & 1 & 6 & 2 & 12 & 4 \\
2 & 6 & 2 & 6 & 1 & 3 & 2 & 6 \\
6 & 2 & 6 & 2 & 3 & 1 & 6 & 2 \\
4 & 12 & 4 & 12 & 2 & 6 & 1 & 3 \\
12 & 4 & 12 & 4 & 6 & 2 & 3 & 1
\end{array}\right)\)
