Atkin-Lehner |
2- 3- 13+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
69264q |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
233472 |
Modular degree for the optimal curve |
Δ |
242727653376 = 212 · 36 · 133 · 37 |
Discriminant |
Eigenvalues |
2- 3- 2 -2 -2 13+ 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243819,46339290] |
[a1,a2,a3,a4,a6] |
Generators |
[282:90:1] |
Generators of the group modulo torsion |
j |
536832589893417/81289 |
j-invariant |
L |
6.8058340424885 |
L(r)(E,1)/r! |
Ω |
0.77316368378495 |
Real period |
R |
2.2006446321522 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000739 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4329a1 7696c1 |
Quadratic twists by: -4 -3 |