Elliptic curves in class 5.1-a over 4.4.11324.1
Isogeny class 5.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 5.1-a1
| \( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 69 a^{3} - 79 a^{2} - 147 a - 47\) , \( 520 a^{3} - 921 a^{2} - 542 a - 57\bigr] \)
|
| 5.1-a2
| \( \bigl[a^{2} + a - 2\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 4 a^{3} + a^{2} - 12 a - 7\) , \( -3 a^{3} + 2 a^{2} + 20 a + 4\bigr] \)
|
| 5.1-a3
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 4 a + 1\) , \( -5 a^{3} - 7 a^{2} + 10 a + 7\) , \( -13 a^{3} - 16 a^{2} + 28 a + 10\bigr] \)
|
| 5.1-a4
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a - 1\) , \( a^{3} - 4 a + 1\) , \( -345 a^{3} - 437 a^{2} + 735 a + 297\) , \( -8879 a^{3} - 11165 a^{2} + 19198 a + 7853\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
