Atkin-Lehner |
2+ 3+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312c |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
216576 |
Modular degree for the optimal curve |
Δ |
-1194127294464 = -1 · 215 · 33 · 13 · 473 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -3 -2 13+ 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14561,-673503] |
[a1,a2,a3,a4,a6] |
Generators |
[321:5256:1] |
Generators of the group modulo torsion |
j |
-10420227679688/36441873 |
j-invariant |
L |
3.8303087911659 |
L(r)(E,1)/r! |
Ω |
0.21725928435081 |
Real period |
R |
4.4075317580551 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000023841 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312be1 58656m1 |
Quadratic twists by: -4 8 |