Atkin-Lehner |
2- 3+ 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112bi |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
86016 |
Modular degree for the optimal curve |
Δ |
-38134001664 = -1 · 212 · 39 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3+ 3 -5 11- -6 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,189,-9342] |
[a1,a2,a3,a4,a6] |
Generators |
[57:432:1] |
Generators of the group modulo torsion |
j |
9261/473 |
j-invariant |
L |
5.4333168736116 |
L(r)(E,1)/r! |
Ω |
0.55180480783567 |
Real period |
R |
1.2308058925318 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002796 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4257b1 68112bd1 |
Quadratic twists by: -4 -3 |