Atkin-Lehner |
2+ 5+ 17+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
51850a |
Isogeny class |
Conductor |
51850 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
46080 |
Modular degree for the optimal curve |
Δ |
331840000000 = 212 · 57 · 17 · 61 |
Discriminant |
Eigenvalues |
2+ 0 5+ -2 0 2 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2167,27741] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:121:1] [-338:1819:8] |
Generators of the group modulo torsion |
j |
72043225281/21237760 |
j-invariant |
L |
6.6531901263893 |
L(r)(E,1)/r! |
Ω |
0.89413202512824 |
Real period |
R |
7.4409482485904 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
10370f1 |
Quadratic twists by: 5 |