Atkin-Lehner |
2- 3+ 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
68112bj |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
307200 |
Modular degree for the optimal curve |
Δ |
-21639341736308736 = -1 · 212 · 33 · 113 · 435 |
Discriminant |
Eigenvalues |
2- 3+ 1 -3 11- -2 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-22587,7197098] |
[a1,a2,a3,a4,a6] |
Generators |
[-227:792:1] [-41:2838:1] |
Generators of the group modulo torsion |
j |
-11523267816003/195668237633 |
j-invariant |
L |
10.3123211947 |
L(r)(E,1)/r! |
Ω |
0.32246144678139 |
Real period |
R |
0.26650010664417 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999946 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4257a1 68112be1 |
Quadratic twists by: -4 -3 |