Atkin-Lehner |
3- 23- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68241c |
Isogeny class |
Conductor |
68241 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
512256 |
Modular degree for the optimal curve |
Δ |
144288538557139467 = 34 · 2310 · 43 |
Discriminant |
Eigenvalues |
1 3- 0 -3 -2 1 -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-145751,11154611] |
[a1,a2,a3,a4,a6] |
Generators |
[-321:5149:1] |
Generators of the group modulo torsion |
j |
8265625/3483 |
j-invariant |
L |
6.505706239654 |
L(r)(E,1)/r! |
Ω |
0.29494218464674 |
Real period |
R |
5.5143911058093 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68241g1 |
Quadratic twists by: -23 |