Atkin-Lehner |
2+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
40768q |
Isogeny class |
Conductor |
40768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-9351200768 = -1 · 221 · 73 · 13 |
Discriminant |
Eigenvalues |
2+ 1 -2 7- -1 13+ -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-289,4927] |
[a1,a2,a3,a4,a6] |
Generators |
[3:-64:1] [9:56:1] |
Generators of the group modulo torsion |
j |
-29791/104 |
j-invariant |
L |
9.3092244922685 |
L(r)(E,1)/r! |
Ω |
1.1352077896729 |
Real period |
R |
1.0250573261735 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40768cs1 1274f1 40768bp1 |
Quadratic twists by: -4 8 -7 |