Atkin-Lehner |
2- 3+ 5+ 7- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
77700f |
Isogeny class |
Conductor |
77700 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
211644580313250000 = 24 · 34 · 56 · 710 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 0 -4 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-165033,-13210938] |
[a1,a2,a3,a4,a6] |
Generators |
[-342:1764:1] |
Generators of the group modulo torsion |
j |
1988376942198784/846578321253 |
j-invariant |
L |
4.739393158518 |
L(r)(E,1)/r! |
Ω |
0.24611109875483 |
Real period |
R |
1.9257128921317 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000175 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3108f1 |
Quadratic twists by: 5 |