Atkin-Lehner |
2+ 5+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
32240b |
Isogeny class |
Conductor |
32240 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
205440 |
Modular degree for the optimal curve |
Δ |
-1007500000000 = -1 · 28 · 510 · 13 · 31 |
Discriminant |
Eigenvalues |
2+ 2 5+ -4 -3 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-415041,-102778195] |
[a1,a2,a3,a4,a6] |
Generators |
[247071513197659061116:-10482271905141559659375:121690642216006592] |
Generators of the group modulo torsion |
j |
-30885724667700265984/3935546875 |
j-invariant |
L |
5.6404498857706 |
L(r)(E,1)/r! |
Ω |
0.094047383669825 |
Real period |
R |
29.987276975044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16120e1 128960bl1 |
Quadratic twists by: -4 8 |