Atkin-Lehner |
3- 13- 59- |
Signs for the Atkin-Lehner involutions |
Class |
89739j |
Isogeny class |
Conductor |
89739 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
8881317260829 = 39 · 133 · 593 |
Discriminant |
Eigenvalues |
0 3- -3 0 -6 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-5304,-39335] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:-266:1] [-65:175:1] |
Generators of the group modulo torsion |
j |
10303307776/5545233 |
j-invariant |
L |
6.9558585627701 |
L(r)(E,1)/r! |
Ω |
0.59559460606472 |
Real period |
R |
0.48661864488793 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000333 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
29913b1 89739g1 |
Quadratic twists by: -3 13 |