Atkin-Lehner |
3+ 11- 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
89001b |
Isogeny class |
Conductor |
89001 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
15680 |
Modular degree for the optimal curve |
Δ |
-267003 = -1 · 33 · 11 · 29 · 31 |
Discriminant |
Eigenvalues |
-2 3+ 0 -2 11- 1 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-135,604] |
[a1,a2,a3,a4,a6] |
Generators |
[7:1:1] |
Generators of the group modulo torsion |
j |
-10077696000/9889 |
j-invariant |
L |
3.2080086543326 |
L(r)(E,1)/r! |
Ω |
3.0838575245419 |
Real period |
R |
0.52012919362963 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999978657 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89001a1 |
Quadratic twists by: -3 |