Atkin-Lehner |
3+ 11- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
57717d |
Isogeny class |
Conductor |
57717 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
7488 |
Modular degree for the optimal curve |
Δ |
-173151 = -1 · 33 · 112 · 53 |
Discriminant |
Eigenvalues |
-1 3+ -3 -3 11- 2 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-89,344] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:25:1] [6:-2:1] |
Generators of the group modulo torsion |
j |
-23613579/53 |
j-invariant |
L |
4.8751025786142 |
L(r)(E,1)/r! |
Ω |
3.2205485336406 |
Real period |
R |
0.75687457085286 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999988 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
57717f1 57717b1 |
Quadratic twists by: -3 -11 |