Atkin-Lehner |
2- 3+ 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
32364c |
Isogeny class |
Conductor |
32364 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-12039408 = -1 · 24 · 33 · 29 · 312 |
Discriminant |
Eigenvalues |
2- 3+ -2 5 1 -1 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-21,-171] |
[a1,a2,a3,a4,a6] |
Generators |
[21:93:1] |
Generators of the group modulo torsion |
j |
-2370816/27869 |
j-invariant |
L |
5.5937599686392 |
L(r)(E,1)/r! |
Ω |
0.96145133444154 |
Real period |
R |
0.4848364627046 |
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 |
129456s1 32364f1 |
Quadratic twists by: -4 -3 |