Atkin-Lehner |
2+ 5+ 31- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
82150a |
Isogeny class |
Conductor |
82150 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
430080 |
Modular degree for the optimal curve |
Δ |
-8149280000000000 = -1 · 214 · 510 · 312 · 53 |
Discriminant |
Eigenvalues |
2+ -1 5+ 0 -2 -5 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-14000,4384000] |
[a1,a2,a3,a4,a6] |
Generators |
[96:-2032:1] [-160:1680:1] |
Generators of the group modulo torsion |
j |
-19423892355841/521553920000 |
j-invariant |
L |
6.1036242428861 |
L(r)(E,1)/r! |
Ω |
0.34695461768867 |
Real period |
R |
2.1989994986154 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000276 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16430c1 |
Quadratic twists by: 5 |