Atkin-Lehner |
2+ 3+ 7+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
90048f |
Isogeny class |
Conductor |
90048 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-415948010688 = -1 · 26 · 32 · 74 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7+ 2 -4 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15785,769251] |
[a1,a2,a3,a4,a6] |
Generators |
[86:201:1] [70:49:1] |
Generators of the group modulo torsion |
j |
-6796808121217024/6499187667 |
j-invariant |
L |
6.5491279905178 |
L(r)(E,1)/r! |
Ω |
0.93956283442841 |
Real period |
R |
0.58086659653445 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000216 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
90048ca1 1407b1 |
Quadratic twists by: -4 8 |