Atkin-Lehner |
2+ 3- 7+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
31122k |
Isogeny class |
Conductor |
31122 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13312 |
Modular degree for the optimal curve |
Δ |
181503504 = 24 · 38 · 7 · 13 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -6 13- 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-288,1840] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:23:1] [-4:56:1] |
Generators of the group modulo torsion |
j |
3630961153/248976 |
j-invariant |
L |
5.405209164005 |
L(r)(E,1)/r! |
Ω |
1.7658640598763 |
Real period |
R |
1.5304714804559 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10374i1 |
Quadratic twists by: -3 |