Elliptic curves in class 8.1-b over 3.3.229.1
Isogeny class 8.1-b contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 8.1-b1
| \( \bigl[a^{2} - 2\) , \( 0\) , \( a + 1\) , \( 2232 a^{2} - 4377 a - 1289\) , \( -519466 a^{2} + 964390 a + 278508\bigr] \)
|
| 8.1-b2
| \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -76 a^{2} + 206 a - 95\) , \( -1041 a^{2} + 2329 a - 271\bigr] \)
|
| 8.1-b3
| \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -106 a^{2} + 176 a - 60\) , \( -971 a^{2} + 2082 a - 692\bigr] \)
|
| 8.1-b4
| \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -a^{2} + a + 5\) , \( -a^{2} + 2\bigr] \)
|
| 8.1-b5
| \( \bigl[1\) , \( -a^{2} - a + 3\) , \( a\) , \( -21 a^{2} + 41 a + 10\) , \( 87 a^{2} - 165 a - 43\bigr] \)
|
| 8.1-b6
| \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -131 a^{2} - 464 a - 415\) , \( -2913 a^{2} - 7754 a - 4350\bigr] \)
|
| 8.1-b7
| \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -26 a^{2} - 59 a - 20\) , \( -163 a^{2} - 344 a - 76\bigr] \)
|
| 8.1-b8
| \( \bigl[1\) , \( -a^{2} + 4\) , \( a^{2} + a - 3\) , \( -6 a^{2} - 9 a + 5\) , \( 10 a^{2} + 21 a + 4\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 6 & 2 & 30 & 10 & 3 & 5 & 15 \\
6 & 1 & 3 & 5 & 15 & 2 & 30 & 10 \\
2 & 3 & 1 & 15 & 5 & 6 & 10 & 30 \\
30 & 5 & 15 & 1 & 3 & 10 & 6 & 2 \\
10 & 15 & 5 & 3 & 1 & 30 & 2 & 6 \\
3 & 2 & 6 & 10 & 30 & 1 & 15 & 5 \\
5 & 30 & 10 & 6 & 2 & 15 & 1 & 3 \\
15 & 10 & 30 & 2 & 6 & 5 & 3 & 1
\end{array}\right)\)
