Atkin-Lehner |
2+ 3+ 5- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
85440j |
Isogeny class |
Conductor |
85440 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
58368 |
Modular degree for the optimal curve |
Δ |
-5132808000 = -1 · 26 · 34 · 53 · 892 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -4 -4 -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-100,3502] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:60:1] [19:90:1] |
Generators of the group modulo torsion |
j |
-1745337664/80200125 |
j-invariant |
L |
8.3226412244434 |
L(r)(E,1)/r! |
Ω |
1.1308730099508 |
Real period |
R |
2.4531611569407 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000134 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
85440t1 42720a2 |
Quadratic twists by: -4 8 |