Atkin-Lehner |
2- 3- 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
31992k |
Isogeny class |
Conductor |
31992 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
342720 |
Modular degree for the optimal curve |
Δ |
-944976417173255664 = -1 · 24 · 33 · 317 · 433 |
Discriminant |
Eigenvalues |
2- 3- 2 0 -1 -2 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-87932,47805525] |
[a1,a2,a3,a4,a6] |
Generators |
[-314:6675:1] |
Generators of the group modulo torsion |
j |
-4699476931881618688/59061026073328479 |
j-invariant |
L |
7.699557592184 |
L(r)(E,1)/r! |
Ω |
0.23680672254299 |
Real period |
R |
5.4190167615044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
63984g1 95976c1 |
Quadratic twists by: -4 -3 |