Atkin-Lehner |
7+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12397a |
Isogeny class |
Conductor |
12397 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
8904 |
Modular degree for the optimal curve |
Δ |
1458494653 = 78 · 11 · 23 |
Discriminant |
Eigenvalues |
2 1 2 7+ 11- 0 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-2172,38203] |
[a1,a2,a3,a4,a6] |
Generators |
[19090:63227:1000] |
Generators of the group modulo torsion |
j |
196661248/253 |
j-invariant |
L |
11.525962477763 |
L(r)(E,1)/r! |
Ω |
1.5096144384509 |
Real period |
R |
7.6350372546722 |
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 |
111573o1 12397r1 |
Quadratic twists by: -3 -7 |