Atkin-Lehner |
2+ 3+ 5- 7- 67- |
Signs for the Atkin-Lehner involutions |
Class |
42210c |
Isogeny class |
Conductor |
42210 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
27146306250000 = 24 · 33 · 58 · 74 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7- -4 -2 -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-7554,-30140] |
[a1,a2,a3,a4,a6] |
Generators |
[-84:122:1] [-79:302:1] |
Generators of the group modulo torsion |
j |
1765725659754363/1005418750000 |
j-invariant |
L |
7.2377446562095 |
L(r)(E,1)/r! |
Ω |
0.55367795644438 |
Real period |
R |
0.40850374820603 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42210n1 |
Quadratic twists by: -3 |