Atkin-Lehner |
2+ 3- 11+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112g |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
812544 |
Modular degree for the optimal curve |
Δ |
-519394695897434544 = -1 · 24 · 329 · 11 · 43 |
Discriminant |
Eigenvalues |
2+ 3- -1 1 11+ 4 5 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-203718,49546159] |
[a1,a2,a3,a4,a6] |
Generators |
[14129774:467136639:97336] |
Generators of the group modulo torsion |
j |
-80161237430634496/44529723585171 |
j-invariant |
L |
6.9951922182617 |
L(r)(E,1)/r! |
Ω |
0.27233880493897 |
Real period |
R |
6.4214060676881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000362 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056i1 22704o1 |
Quadratic twists by: -4 -3 |