Atkin-Lehner |
3- 5+ 11- 101+ |
Signs for the Atkin-Lehner involutions |
Class |
49995d |
Isogeny class |
Conductor |
49995 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
614400 |
Modular degree for the optimal curve |
Δ |
-1112254486083984375 = -1 · 38 · 516 · 11 · 101 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 11- -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1170000,-489453125] |
[a1,a2,a3,a4,a6] |
Generators |
[5502919144797943114862506313918559008430513424253260000:-1264047028921118542209841548229756348932527693167851239375:104701765376765652041813754997678521901886099652608] |
Generators of the group modulo torsion |
j |
-242970740812818720001/1525726318359375 |
j-invariant |
L |
5.8136330865863 |
L(r)(E,1)/r! |
Ω |
0.072553788470766 |
Real period |
R |
80.128594372753 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16665b1 |
Quadratic twists by: -3 |