Atkin-Lehner |
2+ 3+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
15168a |
Isogeny class |
Conductor |
15168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3072 |
Modular degree for the optimal curve |
Δ |
-34947072 = -1 · 214 · 33 · 79 |
Discriminant |
Eigenvalues |
2+ 3+ 0 -1 -3 -5 -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,47,241] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:8:1] [3:20:1] |
Generators of the group modulo torsion |
j |
686000/2133 |
j-invariant |
L |
5.7489217491177 |
L(r)(E,1)/r! |
Ω |
1.457525558662 |
Real period |
R |
0.98607563259382 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15168o1 948c1 45504v1 |
Quadratic twists by: -4 8 -3 |