Atkin-Lehner |
2- 17+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
31552p |
Isogeny class |
Conductor |
31552 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-32309248 = -1 · 216 · 17 · 29 |
Discriminant |
Eigenvalues |
2- -2 -4 1 -4 -1 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-65,319] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:16:1] [7:16:1] |
Generators of the group modulo torsion |
j |
-470596/493 |
j-invariant |
L |
4.6625934187764 |
L(r)(E,1)/r! |
Ω |
1.8900177293165 |
Real period |
R |
0.616739375834 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
31552c1 7888a1 |
Quadratic twists by: -4 8 |