Atkin-Lehner |
2+ 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376d |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
33784128 = 26 · 34 · 73 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 0 -6 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-198,-972] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:6:1] [19:42:1] |
Generators of the group modulo torsion |
j |
39304000/1539 |
j-invariant |
L |
9.3082317478669 |
L(r)(E,1)/r! |
Ω |
1.2752555580932 |
Real period |
R |
3.64955545166 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999992155 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
89376ct1 89376w1 |
Quadratic twists by: -4 -7 |