Atkin-Lehner |
2- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968o |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
622080 |
Modular degree for the optimal curve |
Δ |
134497511407616 = 218 · 78 · 89 |
Discriminant |
Eigenvalues |
2- -2 2 7- 0 4 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-171022472,860793786100] |
[a1,a2,a3,a4,a6] |
j |
135058930188560270934200713/32836306496 |
j-invariant |
L |
1.9110891317081 |
L(r)(E,1)/r! |
Ω |
0.23888614146352 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1246b1 39872bl1 89712bc1 69776s1 |
Quadratic twists by: -4 8 -3 -7 |