Atkin-Lehner |
3+ 11+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
2211d |
Isogeny class |
Conductor |
2211 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
17136 |
Modular degree for the optimal curve |
Δ |
-11516332315851 = -1 · 317 · 113 · 67 |
Discriminant |
Eigenvalues |
-2 3+ -3 -3 11+ -5 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-96152,-11445040] |
[a1,a2,a3,a4,a6] |
Generators |
[442:5675:1] |
Generators of the group modulo torsion |
j |
-98311244861358051328/11516332315851 |
j-invariant |
L |
0.87175521480036 |
L(r)(E,1)/r! |
Ω |
0.13555843610256 |
Real period |
R |
6.4308444377509 |
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 |
35376bi1 6633g1 55275l1 108339n1 |
Quadratic twists by: -4 -3 5 -7 |