Atkin-Lehner |
3- 11- 29+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
89001g |
Isogeny class |
Conductor |
89001 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
52224 |
Modular degree for the optimal curve |
Δ |
76207195251 = 36 · 112 · 29 · 313 |
Discriminant |
Eigenvalues |
1 3- -1 -2 11- 0 -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1140,6857] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:115:1] [14:551:8] |
Generators of the group modulo torsion |
j |
224866629441/104536619 |
j-invariant |
L |
11.735020163303 |
L(r)(E,1)/r! |
Ω |
0.97323087528491 |
Real period |
R |
1.0048164025485 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998868 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9889a1 |
Quadratic twists by: -3 |