Atkin-Lehner |
2+ 3+ 7- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
111552u |
Isogeny class |
Conductor |
111552 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1645056 |
Modular degree for the optimal curve |
Δ |
-3764727091657728 = -1 · 210 · 317 · 73 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 6 -3 -1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1346409,601787313] |
[a1,a2,a3,a4,a6] |
j |
-263605881589063921408/3676491300447 |
j-invariant |
L |
1.2104231626882 |
L(r)(E,1)/r! |
Ω |
0.40347442087404 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
111552dc1 6972e1 |
Quadratic twists by: -4 8 |