Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
4512a |
Isogeny class |
Conductor |
4512 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
5197824 = 212 · 33 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -1 5 -6 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-45,-27] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:4:1] |
Generators of the group modulo torsion |
j |
2515456/1269 |
j-invariant |
L |
3.3319117644499 |
L(r)(E,1)/r! |
Ω |
1.9400879831819 |
Real period |
R |
0.85870120152623 |
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 |
4512f1 9024bp1 13536bc1 112800cc1 |
Quadratic twists by: -4 8 -3 5 |