Elliptic curves in class 25.1-a over 6.6.1387029.1
Isogeny class 25.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 25.1-a1
| \( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 3 a + 3\) , \( 2 a^{5} - 5 a^{4} - 6 a^{3} + 13 a^{2} + 5 a - 3\) , \( a^{3} - 3 a\) , \( -573 a^{5} + 1301 a^{4} + 2097 a^{3} - 3636 a^{2} - 2073 a + 788\) , \( 3182 a^{5} - 7234 a^{4} - 11619 a^{3} + 20192 a^{2} + 11495 a - 4380\bigr] \)
|
| 25.1-a2
| \( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} - 2\) , \( a^{3} - 3 a\) , \( -2 a^{5} + 5 a^{4} + 4 a^{3} - 11 a^{2} - 2 a + 2\) , \( -2 a^{4} + 3 a^{3} + 4 a^{2} - 6 a + 1\bigr] \)
|
| 25.1-a3
| \( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 3 a + 4\) , \( a^{5} - a^{4} - 7 a^{3} + 4 a^{2} + 10 a - 2\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 6 a^{2} - 7 a + 2\) , \( 284 a^{5} - 773 a^{4} - 779 a^{3} + 2337 a^{2} + 354 a - 1029\) , \( 3194 a^{5} - 8705 a^{4} - 8772 a^{3} + 26339 a^{2} + 4016 a - 11678\bigr] \)
|
| 25.1-a4
| \( \bigl[-a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 3 a + 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} - 2\) , \( a^{3} - 3 a\) , \( -17 a^{5} + 50 a^{4} + 29 a^{3} - 131 a^{2} + 28 a + 2\) , \( 36 a^{5} - 117 a^{4} - 33 a^{3} + 298 a^{2} - 140 a + 17\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
