Atkin-Lehner |
2- 3+ 7+ 17- 19- |
Signs for the Atkin-Lehner involutions |
Class |
54264h |
Isogeny class |
Conductor |
54264 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
2062032 = 24 · 3 · 7 · 17 · 192 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -4 -2 17- 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-42959,3441480] |
[a1,a2,a3,a4,a6] |
Generators |
[241:2651:1] [520:11020:1] |
Generators of the group modulo torsion |
j |
547994662986790912/128877 |
j-invariant |
L |
6.9419038029321 |
L(r)(E,1)/r! |
Ω |
1.5347096737896 |
Real period |
R |
18.093073684192 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
108528k1 |
Quadratic twists by: -4 |