Atkin-Lehner |
2- 3+ 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
15624r |
Isogeny class |
Conductor |
15624 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-53578070784 = -1 · 28 · 39 · 73 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- 4 -5 -2 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,324,-10908] |
[a1,a2,a3,a4,a6] |
Generators |
[33:189:1] |
Generators of the group modulo torsion |
j |
746496/10633 |
j-invariant |
L |
6.2656546858291 |
L(r)(E,1)/r! |
Ω |
0.54856380586742 |
Real period |
R |
0.95182708902956 |
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 |
31248a1 124992r1 15624c1 109368bi1 |
Quadratic twists by: -4 8 -3 -7 |