Atkin-Lehner |
2+ 3+ 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312i |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
2561508458496 = 214 · 39 · 132 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 3 -3 3 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4709,99261] |
[a1,a2,a3,a4,a6] |
j |
704988556288/156342069 |
j-invariant |
L |
1.5316068739239 |
L(r)(E,1)/r! |
Ω |
0.76580332645685 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cp1 14664c1 |
Quadratic twists by: -4 8 |