Atkin-Lehner |
2+ 3+ 7+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
49728g |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
430080 |
Modular degree for the optimal curve |
Δ |
7353766504240128 = 210 · 310 · 74 · 373 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7+ 0 2 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-51661,1862173] |
[a1,a2,a3,a4,a6] |
Generators |
[-22020:292219:125] |
Generators of the group modulo torsion |
j |
14890887676143616/7181412601797 |
j-invariant |
L |
6.7019788962312 |
L(r)(E,1)/r! |
Ω |
0.37222435405672 |
Real period |
R |
9.0026066580169 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49728eu1 6216j1 |
Quadratic twists by: -4 8 |