Atkin-Lehner |
2- 3- 23+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344u |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
32640 |
Modular degree for the optimal curve |
Δ |
2792890368 = 213 · 35 · 23 · 61 |
Discriminant |
Eigenvalues |
2- 3- 0 -1 -3 -6 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-608,-5388] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:18:1] [-14:24:1] |
Generators of the group modulo torsion |
j |
6078390625/681858 |
j-invariant |
L |
11.670902796369 |
L(r)(E,1)/r! |
Ω |
0.96832292722506 |
Real period |
R |
0.60263484774646 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8418f1 |
Quadratic twists by: -4 |