Atkin-Lehner |
2+ 3- 7- 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
57288h |
Isogeny class |
Conductor |
57288 |
Conductor |
∏ cp |
224 |
Product of Tamagawa factors cp |
deg |
458752 |
Modular degree for the optimal curve |
Δ |
91555728005527632 = 24 · 37 · 78 · 114 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- 11+ 2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-119439,6323670] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:-3087:1] |
Generators of the group modulo torsion |
j |
11777302808405358592/5722233000345477 |
j-invariant |
L |
6.1751144414209 |
L(r)(E,1)/r! |
Ω |
0.30137009172879 |
Real period |
R |
0.36589530204187 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000015 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
114576h1 |
Quadratic twists by: -4 |