Elliptic curves in class 21.1-a over 3.3.321.1
Isogeny class 21.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 21.1-a1
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 2\) , \( 332 a^{2} - 279 a - 1437\) , \( 5695 a^{2} - 4506 a - 24104\bigr] \)
|
| 21.1-a2
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 2\) , \( 22 a^{2} + a - 87\) , \( 161 a^{2} - 10 a - 516\bigr] \)
|
| 21.1-a3
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 2\) , \( 17 a^{2} - 19 a - 82\) , \( 118 a^{2} - 90 a - 494\bigr] \)
|
| 21.1-a4
| \( \bigl[a^{2} - 2\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 2\) , \( -3 a^{2} - 4 a + 3\) , \( 3 a^{2} - a - 11\bigr] \)
|
| 21.1-a5
| \( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( -13 a^{2} - 14 a + 11\) , \( -19 a^{2} - 37 a + 11\bigr] \)
|
| 21.1-a6
| \( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( -108 a^{2} - 54 a + 26\) , \( -3207 a^{2} - 4661 a + 1299\bigr] \)
|
| 21.1-a7
| \( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( -148 a^{2} - 149 a + 51\) , \( -1877 a^{2} - 3047 a + 837\bigr] \)
|
| 21.1-a8
| \( \bigl[a\) , \( -a^{2} + 2 a + 4\) , \( a^{2} - 3\) , \( -2348 a^{2} - 2404 a + 716\) , \( -111419 a^{2} - 180773 a + 49599\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 2 & 4 & 12 & 12 & 6 & 3 \\
4 & 1 & 2 & 4 & 12 & 3 & 6 & 12 \\
2 & 2 & 1 & 2 & 6 & 6 & 3 & 6 \\
4 & 4 & 2 & 1 & 3 & 12 & 6 & 12 \\
12 & 12 & 6 & 3 & 1 & 4 & 2 & 4 \\
12 & 3 & 6 & 12 & 4 & 1 & 2 & 4 \\
6 & 6 & 3 & 6 & 2 & 2 & 1 & 2 \\
3 & 12 & 6 & 12 & 4 & 4 & 2 & 1
\end{array}\right)\)
