Atkin-Lehner |
2+ 5+ 17+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
51850b |
Isogeny class |
Conductor |
51850 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
78336 |
Modular degree for the optimal curve |
Δ |
-117000147200 = -1 · 28 · 52 · 173 · 612 |
Discriminant |
Eigenvalues |
2+ 1 5+ -3 0 -3 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-9761,370708] |
[a1,a2,a3,a4,a6] |
Generators |
[-92:747:1] [43:154:1] |
Generators of the group modulo torsion |
j |
-4113416461755505/4680005888 |
j-invariant |
L |
7.655170738709 |
L(r)(E,1)/r! |
Ω |
1.0462607849095 |
Real period |
R |
1.8291736747473 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51850z1 |
Quadratic twists by: 5 |