Atkin-Lehner |
2+ 7+ 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
89782b |
Isogeny class |
Conductor |
89782 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-4711161771008 = -1 · 210 · 72 · 116 · 53 |
Discriminant |
Eigenvalues |
2+ -1 -2 7+ 11- -5 1 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1696,-108544] |
[a1,a2,a3,a4,a6] |
Generators |
[160:1856:1] [64:192:1] |
Generators of the group modulo torsion |
j |
-304821217/2659328 |
j-invariant |
L |
5.3309533570195 |
L(r)(E,1)/r! |
Ω |
0.32615258043801 |
Real period |
R |
2.0431209490927 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999990082 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
742g1 |
Quadratic twists by: -11 |