Atkin-Lehner |
2- 3- 5- 7- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
89040cs |
Isogeny class |
Conductor |
89040 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
8116540884910080 = 222 · 39 · 5 · 7 · 532 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 2 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-238680,-44751852] |
[a1,a2,a3,a4,a6] |
Generators |
[-297:162:1] |
Generators of the group modulo torsion |
j |
367124756298856921/1981577364480 |
j-invariant |
L |
10.354437504353 |
L(r)(E,1)/r! |
Ω |
0.21606604706608 |
Real period |
R |
2.6623642892334 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003391 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11130i1 |
Quadratic twists by: -4 |