Elliptic curves in class 25.1-a over 4.4.4205.1
Isogeny class 25.1-a contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 25.1-a1
| \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( 19 a^{3} - 44 a^{2} - 39 a\) , \( -12 a^{3} + 116 a^{2} - 392 a - 305\bigr] \)
|
| 25.1-a2
| \( \bigl[-a^{3} + 2 a^{2} + 3 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a^{2} - a - 1\) , \( 6 a^{3} - 6 a^{2} - 28 a - 8\) , \( 12 a^{3} - 10 a^{2} - 58 a - 33\bigr] \)
|
| 25.1-a3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a\) , \( -5 a^{3} + 9 a^{2} + 20 a - 8\) , \( 12 a^{3} - 19 a^{2} - 46 a + 18\bigr] \)
|
| 25.1-a4
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( 18 a^{3} - 41 a^{2} - 40 a - 5\) , \( -519 a^{3} + 1336 a^{2} + 482 a - 388\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 15 & 3 & 5 \\
15 & 1 & 5 & 3 \\
3 & 5 & 1 & 15 \\
5 & 3 & 15 & 1
\end{array}\right)\)
