Atkin-Lehner |
3+ 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
1311a |
Isogeny class |
Conductor |
1311 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
780 |
Modular degree for the optimal curve |
Δ |
271377 = 33 · 19 · 232 |
Discriminant |
Eigenvalues |
-1 3+ -2 0 -4 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-5654,161282] |
[a1,a2,a3,a4,a6] |
j |
19989223566735457/271377 |
j-invariant |
L |
0.27407827464521 |
L(r)(E,1)/r! |
Ω |
2.1926261971617 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
20976j1 83904p1 3933a1 32775t1 |
Quadratic twists by: -4 8 -3 5 |