Atkin-Lehner |
2+ 31+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
117242a |
Isogeny class |
Conductor |
117242 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
252480 |
Modular degree for the optimal curve |
Δ |
13745686564 = 22 · 314 · 612 |
Discriminant |
Eigenvalues |
2+ -3 -3 -3 -3 -3 -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1141,-13439] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:27:1] [-21:41:1] [-18:41:1] |
Generators of the group modulo torsion |
j |
177970473/14884 |
j-invariant |
L |
5.9093159394293 |
L(r)(E,1)/r! |
Ω |
0.82578134967578 |
Real period |
R |
0.59633581593331 |
Regulator |
r |
3 |
Rank of the group of rational points |
S |
1.0000000000224 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117242e1 |
Quadratic twists by: -31 |