Atkin-Lehner |
2- 3+ 7+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
50232r |
Isogeny class |
Conductor |
50232 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-1014938688913968 = -1 · 24 · 3 · 72 · 138 · 232 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ -4 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,16401,-1307712] |
[a1,a2,a3,a4,a6] |
Generators |
[77:637:1] [353:6953:1] |
Generators of the group modulo torsion |
j |
30492163182184448/63433668057123 |
j-invariant |
L |
6.9723734343627 |
L(r)(E,1)/r! |
Ω |
0.2566973790761 |
Real period |
R |
6.7904602877699 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
100464s1 |
Quadratic twists by: -4 |