Atkin-Lehner |
2+ 3+ 5- 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
47970b |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
215040 |
Modular degree for the optimal curve |
Δ |
-6041917440000 = -1 · 214 · 33 · 54 · 13 · 412 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 -4 13+ -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-131199,18324493] |
[a1,a2,a3,a4,a6] |
Generators |
[197:-406:1] [89:2666:1] |
Generators of the group modulo torsion |
j |
-9250248173567332203/223774720000 |
j-invariant |
L |
7.4159095340051 |
L(r)(E,1)/r! |
Ω |
0.70016252433286 |
Real period |
R |
1.3239621652617 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999977 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47970v1 |
Quadratic twists by: -3 |