Atkin-Lehner |
2+ 3+ 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
4758b |
Isogeny class |
Conductor |
4758 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
960 |
Modular degree for the optimal curve |
Δ |
114192 = 24 · 32 · 13 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -4 0 -4 13- -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-12,0] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:4:1] [-3:6:1] |
Generators of the group modulo torsion |
j |
217081801/114192 |
j-invariant |
L |
2.6840598698196 |
L(r)(E,1)/r! |
Ω |
2.9210647930051 |
Real period |
R |
0.91886351725166 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999996 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
38064be1 14274t1 118950bn1 61854n1 |
Quadratic twists by: -4 -3 5 13 |