Atkin-Lehner |
2+ 3- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
6138g |
Isogeny class |
Conductor |
6138 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-12511894044672 = -1 · 224 · 37 · 11 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 11- -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-12096,-536576] |
[a1,a2,a3,a4,a6] |
Generators |
[151280634240:-721476975808:1108717875] |
Generators of the group modulo torsion |
j |
-268498407453697/17163091968 |
j-invariant |
L |
3.4075868072858 |
L(r)(E,1)/r! |
Ω |
0.2267803037199 |
Real period |
R |
15.025938105695 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
49104bh1 2046g1 67518bn1 |
Quadratic twists by: -4 -3 -11 |