Atkin-Lehner |
2+ 3- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
117312be |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
36 |
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 |
[-89:1128:1] |
Generators of the group modulo torsion |
j |
-10420227679688/36441873 |
j-invariant |
L |
9.350226805691 |
L(r)(E,1)/r! |
Ω |
0.869020990938 |
Real period |
R |
0.29887485452674 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005122 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117312c1 58656r1 |
Quadratic twists by: -4 8 |