Atkin-Lehner |
2- 3- 5+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
85140m |
Isogeny class |
Conductor |
85140 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
6881760 |
Modular degree for the optimal curve |
Δ |
318783316500000000 = 28 · 36 · 59 · 11 · 433 |
Discriminant |
Eigenvalues |
2- 3- 5+ 2 11- 5 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-99744528,-383426152652] |
[a1,a2,a3,a4,a6] |
Generators |
[-26118411626631111788891609550509085:128935636986495348742305587156639:4529704916063277141444553368375] |
Generators of the group modulo torsion |
j |
588062461101756601532416/1708158203125 |
j-invariant |
L |
7.0304042367881 |
L(r)(E,1)/r! |
Ω |
0.047772424734184 |
Real period |
R |
49.054828009441 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9460d1 |
Quadratic twists by: -3 |