Atkin-Lehner |
2+ 3+ 7+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
49728d |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
16498556928 = 218 · 35 · 7 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 0 2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-83937,-9332127] |
[a1,a2,a3,a4,a6] |
Generators |
[-478820641136390:1084501380761:2869341461000] |
Generators of the group modulo torsion |
j |
249487788397177/62937 |
j-invariant |
L |
5.9470601464606 |
L(r)(E,1)/r! |
Ω |
0.28048572893897 |
Real period |
R |
21.202719186276 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000016 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49728eq1 777e1 |
Quadratic twists by: -4 8 |