Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
77064d |
Isogeny class |
Conductor |
77064 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
-32962548962304 = -1 · 210 · 33 · 137 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 3 5 -2 13+ 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-248824,47857276] |
[a1,a2,a3,a4,a6] |
Generators |
[-30:7436:1] |
Generators of the group modulo torsion |
j |
-344700718852/6669 |
j-invariant |
L |
8.6133210171905 |
L(r)(E,1)/r! |
Ω |
0.6042363118691 |
Real period |
R |
1.7818610132371 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002295 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5928l1 |
Quadratic twists by: 13 |