Atkin-Lehner |
2+ 11+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
49984d |
Isogeny class |
Conductor |
49984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
473088 |
Modular degree for the optimal curve |
Δ |
558083218604032 = 229 · 114 · 71 |
Discriminant |
Eigenvalues |
2+ 3 0 -1 11+ 5 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-275500,55646768] |
[a1,a2,a3,a4,a6] |
Generators |
[7986:5120:27] |
Generators of the group modulo torsion |
j |
8821625150390625/2128918528 |
j-invariant |
L |
10.974671527782 |
L(r)(E,1)/r! |
Ω |
0.50535067144819 |
Real period |
R |
2.714617825742 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000064 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49984t1 1562c1 |
Quadratic twists by: -4 8 |