Atkin-Lehner |
2+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
42350t |
Isogeny class |
Conductor |
42350 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
403200 |
Modular degree for the optimal curve |
Δ |
-18649831621093750 = -1 · 2 · 510 · 72 · 117 |
Discriminant |
Eigenvalues |
2+ 0 5+ 7- 11- 3 -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-278867,-56991709] |
[a1,a2,a3,a4,a6] |
Generators |
[7482631:427293173:2197] |
Generators of the group modulo torsion |
j |
-138630825/1078 |
j-invariant |
L |
4.1440482868336 |
L(r)(E,1)/r! |
Ω |
0.10382897560651 |
Real period |
R |
9.9780631144214 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42350ct1 3850m1 |
Quadratic twists by: 5 -11 |