Atkin-Lehner |
2+ 3- 23- 31- |
Signs for the Atkin-Lehner involutions |
Class |
4278k |
Isogeny class |
Conductor |
4278 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
99840 |
Modular degree for the optimal curve |
Δ |
-9731978676928512 = -1 · 226 · 38 · 23 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 4 4 -2 2 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-220724,40176434] |
[a1,a2,a3,a4,a6] |
j |
-1189240134686977282489/9731978676928512 |
j-invariant |
L |
3.2850588673755 |
L(r)(E,1)/r! |
Ω |
0.41063235842194 |
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 |
34224t1 12834q1 106950br1 98394be1 |
Quadratic twists by: -4 -3 5 -23 |