Atkin-Lehner |
5+ 7- 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
61985i |
Isogeny class |
Conductor |
61985 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
333312 |
Modular degree for the optimal curve |
Δ |
-40359281725984375 = -1 · 56 · 79 · 112 · 232 |
Discriminant |
Eigenvalues |
-1 0 5+ 7- 11- 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,82727,-3110544] |
[a1,a2,a3,a4,a6] |
Generators |
[48:960:1] [60:1407:1] |
Generators of the group modulo torsion |
j |
1551629757033/1000140625 |
j-invariant |
L |
6.1539276097692 |
L(r)(E,1)/r! |
Ω |
0.20765204571906 |
Real period |
R |
7.4089417087687 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
61985q1 |
Quadratic twists by: -7 |