Atkin-Lehner |
2- 3- 13- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
67938u |
Isogeny class |
Conductor |
67938 |
Conductor |
∏ cp |
224 |
Product of Tamagawa factors cp |
deg |
494592 |
Modular degree for the optimal curve |
Δ |
-21097625223168 = -1 · 216 · 37 · 133 · 67 |
Discriminant |
Eigenvalues |
2- 3- -4 -4 -3 13- 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-64230,6264036] |
[a1,a2,a3,a4,a6] |
Generators |
[-276:1866:1] [300:3594:1] |
Generators of the group modulo torsion |
j |
-13338526128308893/9602924544 |
j-invariant |
L |
12.84682962892 |
L(r)(E,1)/r! |
Ω |
0.67508453354849 |
Real period |
R |
0.084955165073736 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999844 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67938k1 |
Quadratic twists by: 13 |