Atkin-Lehner |
7+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
19747a |
Isogeny class |
Conductor |
19747 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
69216 |
Modular degree for the optimal curve |
Δ |
-69210892196173 = -1 · 78 · 13 · 314 |
Discriminant |
Eigenvalues |
-1 0 -4 7+ 3 13+ -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-10912,596600] |
[a1,a2,a3,a4,a6] |
Generators |
[80:440:1] |
Generators of the group modulo torsion |
j |
-24923851281/12005773 |
j-invariant |
L |
1.4796909991834 |
L(r)(E,1)/r! |
Ω |
0.57555229048477 |
Real period |
R |
1.2854531409624 |
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 |
19747c1 |
Quadratic twists by: -7 |