Atkin-Lehner |
2+ 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
50024b |
Isogeny class |
Conductor |
50024 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
139776 |
Modular degree for the optimal curve |
Δ |
7726601389312 = 28 · 138 · 37 |
Discriminant |
Eigenvalues |
2+ -1 0 -3 5 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-66473,6617389] |
[a1,a2,a3,a4,a6] |
Generators |
[165:-338:1] |
Generators of the group modulo torsion |
j |
26288512000/6253 |
j-invariant |
L |
4.6441029441486 |
L(r)(E,1)/r! |
Ω |
0.72172849725007 |
Real period |
R |
0.80433690817693 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999953 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
100048a1 3848b1 |
Quadratic twists by: -4 13 |