Atkin-Lehner |
3- 7- 13- 61- |
Signs for the Atkin-Lehner involutions |
Class |
49959k |
Isogeny class |
Conductor |
49959 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
-186701629023 = -1 · 37 · 72 · 134 · 61 |
Discriminant |
Eigenvalues |
-1 3- -2 7- -4 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,1174,-14160] |
[a1,a2,a3,a4,a6] |
Generators |
[20:120:1] |
Generators of the group modulo torsion |
j |
245667233447/256106487 |
j-invariant |
L |
2.981785091076 |
L(r)(E,1)/r! |
Ω |
0.54762987840262 |
Real period |
R |
2.7224455865635 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000007 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
16653f1 |
Quadratic twists by: -3 |