Atkin-Lehner |
2+ 3+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
19266b |
Isogeny class |
Conductor |
19266 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
381888 |
Modular degree for the optimal curve |
Δ |
-2200081667983540224 = -1 · 217 · 3 · 138 · 193 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 -4 13+ -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-843144,-306767040] |
[a1,a2,a3,a4,a6] |
Generators |
[286324667:5594202189:226981] |
Generators of the group modulo torsion |
j |
-81261149221993/2697068544 |
j-invariant |
L |
2.8999203404762 |
L(r)(E,1)/r! |
Ω |
0.07862249341999 |
Real period |
R |
12.294701826975 |
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 |
57798bi1 19266s1 |
Quadratic twists by: -3 13 |