Atkin-Lehner |
2- 3+ 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
40584u |
Isogeny class |
Conductor |
40584 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
112896 |
Modular degree for the optimal curve |
Δ |
169199699926032 = 24 · 37 · 193 · 893 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 -2 -5 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14084,-144447] |
[a1,a2,a3,a4,a6] |
Generators |
[312:-5073:1] [-44:623:1] |
Generators of the group modulo torsion |
j |
19311349076038912/10574981245377 |
j-invariant |
L |
6.9002533023226 |
L(r)(E,1)/r! |
Ω |
0.46821619829056 |
Real period |
R |
0.81874016124219 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81168x1 121752s1 |
Quadratic twists by: -4 -3 |