Atkin-Lehner |
2+ 3+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112b |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
145152 |
Modular degree for the optimal curve |
Δ |
-43801236308016 = -1 · 24 · 33 · 119 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ 1 1 11- -6 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3642,329467] |
[a1,a2,a3,a4,a6] |
Generators |
[226:3993:8] |
Generators of the group modulo torsion |
j |
-12366869833728/101391750713 |
j-invariant |
L |
6.9470037305979 |
L(r)(E,1)/r! |
Ω |
0.54907299519678 |
Real period |
R |
0.70290226448568 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000211 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056n1 68112a1 |
Quadratic twists by: -4 -3 |