Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264h |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-21891000238848 = -1 · 28 · 37 · 134 · 372 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 4 13+ 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18615,1003142] |
[a1,a2,a3,a4,a6] |
Generators |
[-47:1332:1] |
Generators of the group modulo torsion |
j |
-3822481042000/117300027 |
j-invariant |
L |
6.6843413188857 |
L(r)(E,1)/r! |
Ω |
0.67622310447339 |
Real period |
R |
1.2356020657826 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000052 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34632m2 23088c2 |
Quadratic twists by: -4 -3 |