Atkin-Lehner |
2- 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312cm |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
11 |
Product of Tamagawa factors cp |
deg |
2280960 |
Modular degree for the optimal curve |
Δ |
-5712590883916717632 = -1 · 26 · 311 · 133 · 475 |
Discriminant |
Eigenvalues |
2- 3- 0 3 5 13+ -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-241788,-123845346] |
[a1,a2,a3,a4,a6] |
Generators |
[83085:23948532:1] |
Generators of the group modulo torsion |
j |
-24425854348032136000/89259232561198713 |
j-invariant |
L |
10.345016790193 |
L(r)(E,1)/r! |
Ω |
0.098641524741112 |
Real period |
R |
9.5340788183681 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000202 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312br1 58656o1 |
Quadratic twists by: -4 8 |