Atkin-Lehner |
3- 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
31407c |
Isogeny class |
Conductor |
31407 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
65664 |
Modular degree for the optimal curve |
Δ |
13298129861103 = 33 · 198 · 29 |
Discriminant |
Eigenvalues |
1 3- 2 -4 -2 2 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-6145,59369] |
[a1,a2,a3,a4,a6] |
Generators |
[391:7385:1] |
Generators of the group modulo torsion |
j |
1510633/783 |
j-invariant |
L |
7.7645315526353 |
L(r)(E,1)/r! |
Ω |
0.62308935957619 |
Real period |
R |
1.3845939026424 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
94221h1 31407b1 |
Quadratic twists by: -3 -19 |