Atkin-Lehner |
3+ 13- 89- |
Signs for the Atkin-Lehner involutions |
Class |
45123h |
Isogeny class |
Conductor |
45123 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
24000 |
Modular degree for the optimal curve |
Δ |
1759797 = 32 · 133 · 89 |
Discriminant |
Eigenvalues |
-2 3+ -4 -5 -2 13- -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-30,2] |
[a1,a2,a3,a4,a6] |
Generators |
[0:-2:1] [-38:27:8] [-4:6:1] |
Generators of the group modulo torsion |
j |
1404928/801 |
j-invariant |
L |
4.2417473525854 |
L(r)(E,1)/r! |
Ω |
2.2008197466491 |
Real period |
R |
0.48183720623233 |
Regulator |
r |
3 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45123g1 |
Quadratic twists by: 13 |