Atkin-Lehner |
2- 3- 31- 47- |
Signs for the Atkin-Lehner involutions |
Class |
69936bc |
Isogeny class |
Conductor |
69936 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1460160 |
Modular degree for the optimal curve |
Δ |
-563785727213568 = -1 · 227 · 3 · 313 · 47 |
Discriminant |
Eigenvalues |
2- 3- -4 -3 0 -4 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3138000,2138529684] |
[a1,a2,a3,a4,a6] |
Generators |
[27030:31744:27] |
Generators of the group modulo torsion |
j |
-834300915814216242001/137642999808 |
j-invariant |
L |
3.7709065597925 |
L(r)(E,1)/r! |
Ω |
0.40665398115373 |
Real period |
R |
0.77275085915571 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8742g1 |
Quadratic twists by: -4 |