Atkin-Lehner |
3- 23- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68241k |
Isogeny class |
Conductor |
68241 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
684288 |
Modular degree for the optimal curve |
Δ |
-18678814520209401 = -1 · 3 · 238 · 433 |
Discriminant |
Eigenvalues |
1 3- -3 -1 5 3 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-148925,-23089675] |
[a1,a2,a3,a4,a6] |
j |
-2467489596697/126177609 |
j-invariant |
L |
1.4538443556716 |
L(r)(E,1)/r! |
Ω |
0.12115369589364 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2967b1 |
Quadratic twists by: -23 |