Atkin-Lehner |
2- 3+ 43+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
12126f |
Isogeny class |
Conductor |
12126 |
Conductor |
∏ cp |
58 |
Product of Tamagawa factors cp |
deg |
109968 |
Modular degree for the optimal curve |
Δ |
-18055753138962432 = -1 · 229 · 32 · 433 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 2 -1 6 -2 -3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,47843,-5036941] |
[a1,a2,a3,a4,a6] |
Generators |
[119:1476:1] |
Generators of the group modulo torsion |
j |
12110954087296924847/18055753138962432 |
j-invariant |
L |
6.9490104930214 |
L(r)(E,1)/r! |
Ω |
0.20547834428542 |
Real period |
R |
0.58308103541717 |
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 |
97008z1 36378b1 |
Quadratic twists by: -4 -3 |