Atkin-Lehner |
2+ 3+ 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
63168r |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
746496 |
Modular degree for the optimal curve |
Δ |
-611633761309605888 = -1 · 214 · 39 · 79 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- -3 -2 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-924533,-343916691] |
[a1,a2,a3,a4,a6] |
j |
-5334227016064000000/37331162189307 |
j-invariant |
L |
0.69254797669398 |
L(r)(E,1)/r! |
Ω |
0.076949775220542 |
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 |
63168db1 3948e1 |
Quadratic twists by: -4 8 |