Atkin-Lehner |
2+ 3+ 5- 13- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
50310f |
Isogeny class |
Conductor |
50310 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
344064 |
Modular degree for the optimal curve |
Δ |
-26582999040000 = -1 · 216 · 33 · 54 · 13 · 432 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 -4 13- 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-275199,-55498995] |
[a1,a2,a3,a4,a6] |
Generators |
[1374:45777:1] |
Generators of the group modulo torsion |
j |
-85369235064361060203/984555520000 |
j-invariant |
L |
3.4206704010194 |
L(r)(E,1)/r! |
Ω |
0.10422153653245 |
Real period |
R |
4.1026434108435 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000107 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
50310bl1 |
Quadratic twists by: -3 |