Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
13536a |
Isogeny class |
Conductor |
13536 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1536 |
Modular degree for the optimal curve |
Δ |
5197824 = 212 · 33 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 1 1 -1 4 -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-72,208] |
[a1,a2,a3,a4,a6] |
Generators |
[8:12:1] |
Generators of the group modulo torsion |
j |
373248/47 |
j-invariant |
L |
5.3205863504265 |
L(r)(E,1)/r! |
Ω |
2.3348637491626 |
Real period |
R |
0.56968916840808 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13536t1 27072b1 13536v1 |
Quadratic twists by: -4 8 -3 |