Atkin-Lehner |
2- 5+ 29- 47- |
Signs for the Atkin-Lehner involutions |
Class |
68150w |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
1746302860000000 = 28 · 57 · 292 · 473 |
Discriminant |
Eigenvalues |
2- -3 5+ -3 1 -1 -6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-51630,4055997] |
[a1,a2,a3,a4,a6] |
Generators |
[-211:2455:1] [-111:2955:1] |
Generators of the group modulo torsion |
j |
974096931523689/111763383040 |
j-invariant |
L |
8.9916273344427 |
L(r)(E,1)/r! |
Ω |
0.45606779131855 |
Real period |
R |
0.10268515615075 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13630b1 |
Quadratic twists by: 5 |