Atkin-Lehner |
2- 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
4512m |
Isogeny class |
Conductor |
4512 |
Conductor |
∏ cp |
26 |
Product of Tamagawa factors cp |
deg |
3328 |
Modular degree for the optimal curve |
Δ |
306926309376 = 212 · 313 · 47 |
Discriminant |
Eigenvalues |
2- 3- -1 1 -3 2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2781,48843] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:324:1] |
Generators of the group modulo torsion |
j |
580928771584/74933181 |
j-invariant |
L |
4.2403685486336 |
L(r)(E,1)/r! |
Ω |
0.93392947940983 |
Real period |
R |
0.17462892179764 |
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 |
4512d1 9024c1 13536m1 112800i1 |
Quadratic twists by: -4 8 -3 5 |