Atkin-Lehner |
2- 7+ 13+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
13286h |
Isogeny class |
Conductor |
13286 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13056 |
Modular degree for the optimal curve |
Δ |
-287402752 = -1 · 28 · 7 · 133 · 73 |
Discriminant |
Eigenvalues |
2- 0 4 7+ -3 13+ -1 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-3448,-77061] |
[a1,a2,a3,a4,a6] |
Generators |
[69:65:1] |
Generators of the group modulo torsion |
j |
-4532182556825169/287402752 |
j-invariant |
L |
8.3030819641048 |
L(r)(E,1)/r! |
Ω |
0.31151999922467 |
Real period |
R |
3.3316809453527 |
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 |
106288r1 119574i1 93002p1 |
Quadratic twists by: -4 -3 -7 |