Atkin-Lehner |
2+ 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
123786b |
Isogeny class |
Conductor |
123786 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
197120 |
Modular degree for the optimal curve |
Δ |
-831369552624 = -1 · 24 · 33 · 13 · 236 |
Discriminant |
Eigenvalues |
2+ 3+ 2 2 4 13+ 0 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1686,-50908] |
[a1,a2,a3,a4,a6] |
j |
-132651/208 |
j-invariant |
L |
2.8247807361371 |
L(r)(E,1)/r! |
Ω |
0.35309770656266 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
123786x1 234c1 |
Quadratic twists by: -3 -23 |