Atkin-Lehner |
2+ 3+ 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
48642b |
Isogeny class |
Conductor |
48642 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
587520 |
Modular degree for the optimal curve |
Δ |
31296065529839616 = 217 · 38 · 112 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ -1 1 11- 6 -5 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-374893,-88095971] |
[a1,a2,a3,a4,a6] |
j |
48157301805552254689/258645169668096 |
j-invariant |
L |
0.38600505914165 |
L(r)(E,1)/r! |
Ω |
0.19300252945186 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48642p1 |
Quadratic twists by: -11 |