Atkin-Lehner |
2- 3- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31248cd |
Isogeny class |
Conductor |
31248 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
8064999838973952 = 218 · 310 · 75 · 31 |
Discriminant |
Eigenvalues |
2- 3- -4 7- -2 -2 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1566507,754639450] |
[a1,a2,a3,a4,a6] |
Generators |
[82945:338688:125] [-1003:36288:1] |
Generators of the group modulo torsion |
j |
142374842119352809/2700952128 |
j-invariant |
L |
6.8755498976251 |
L(r)(E,1)/r! |
Ω |
0.38188054471883 |
Real period |
R |
0.90022259482851 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3906r1 124992gh1 10416bm1 |
Quadratic twists by: -4 8 -3 |