Atkin-Lehner |
2+ 3- 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69360z |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
348160 |
Modular degree for the optimal curve |
Δ |
-2305348319101680 = -1 · 24 · 35 · 5 · 179 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -1 3 6 17+ 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,11464,2265075] |
[a1,a2,a3,a4,a6] |
j |
87808/1215 |
j-invariant |
L |
3.4128899344545 |
L(r)(E,1)/r! |
Ω |
0.34128899431223 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34680b1 69360r1 |
Quadratic twists by: -4 17 |