Atkin-Lehner |
2- 3+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312cd |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
29184 |
Modular degree for the optimal curve |
Δ |
-180191232 = -1 · 215 · 32 · 13 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 2 13- -5 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-33,-639] |
[a1,a2,a3,a4,a6] |
Generators |
[27:132:1] |
Generators of the group modulo torsion |
j |
-125000/5499 |
j-invariant |
L |
7.0690874436747 |
L(r)(E,1)/r! |
Ω |
0.78823476973777 |
Real period |
R |
2.2420628014672 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000027537 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312cx1 58656i1 |
Quadratic twists by: -4 8 |