Atkin-Lehner |
3- 5+ 7- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
22365d |
Isogeny class |
Conductor |
22365 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-28888800609375 = -1 · 312 · 56 · 72 · 71 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- -4 0 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9473,441456] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:867:1] |
Generators of the group modulo torsion |
j |
-128948357570761/39627984375 |
j-invariant |
L |
2.8997554296269 |
L(r)(E,1)/r! |
Ω |
0.62793011841444 |
Real period |
R |
1.1544897053787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7455c1 111825e1 |
Quadratic twists by: -3 5 |