Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825s |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
207360 |
Modular degree for the optimal curve |
Δ |
-248855208984375 = -1 · 3 · 59 · 76 · 192 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- -2 -4 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,1812,759156] |
[a1,a2,a3,a4,a6] |
Generators |
[-60:692:1] |
Generators of the group modulo torsion |
j |
357911/135375 |
j-invariant |
L |
2.9204855291511 |
L(r)(E,1)/r! |
Ω |
0.43061381462169 |
Real period |
R |
3.391072731211 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000885 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13965x1 1425g1 |
Quadratic twists by: 5 -7 |