Atkin-Lehner |
3- 11+ 19- 37- |
Signs for the Atkin-Lehner involutions |
Class |
69597d |
Isogeny class |
Conductor |
69597 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
31104 |
Modular degree for the optimal curve |
Δ |
682120197 = 36 · 113 · 19 · 37 |
Discriminant |
Eigenvalues |
0 3- 0 -4 11+ -4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-1380,-19692] |
[a1,a2,a3,a4,a6] |
Generators |
[-22:4:1] [54:251:1] |
Generators of the group modulo torsion |
j |
398688256000/935693 |
j-invariant |
L |
7.2884498506588 |
L(r)(E,1)/r! |
Ω |
0.78341346116466 |
Real period |
R |
4.6517262033359 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999955 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7733d1 |
Quadratic twists by: -3 |