Atkin-Lehner |
7- 19- 73- |
Signs for the Atkin-Lehner involutions |
Class |
9709d |
Isogeny class |
Conductor |
9709 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
9504 |
Modular degree for the optimal curve |
Δ |
171742501 = 73 · 193 · 73 |
Discriminant |
Eigenvalues |
-2 -3 -1 7- -2 0 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-523,4560] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:66:1] [12:3:1] |
Generators of the group modulo torsion |
j |
15820812324864/171742501 |
j-invariant |
L |
2.0953036621421 |
L(r)(E,1)/r! |
Ω |
1.8161351379647 |
Real period |
R |
0.12819063578976 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
87381k1 67963f1 |
Quadratic twists by: -3 -7 |