Atkin-Lehner |
2- 3+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384bt |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
100758528 = 210 · 32 · 13 · 292 |
Discriminant |
Eigenvalues |
2- 3+ 0 -2 2 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-133,-299] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:8:1] |
Generators of the group modulo torsion |
j |
256000000/98397 |
j-invariant |
L |
4.8770400609992 |
L(r)(E,1)/r! |
Ω |
1.451390982747 |
Real period |
R |
1.6801262096606 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996774 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384bb1 18096bd1 |
Quadratic twists by: -4 8 |