Atkin-Lehner |
2+ 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112f |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
13440 |
Modular degree for the optimal curve |
Δ |
-353092608 = -1 · 210 · 36 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 11+ 2 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-75,938] |
[a1,a2,a3,a4,a6] |
Generators |
[11:38:1] |
Generators of the group modulo torsion |
j |
-62500/473 |
j-invariant |
L |
6.4093743324335 |
L(r)(E,1)/r! |
Ω |
1.4618820105948 |
Real period |
R |
2.1921654025437 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999682 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056w1 7568f1 |
Quadratic twists by: -4 -3 |