Atkin-Lehner |
3- 23- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
84111b |
Isogeny class |
Conductor |
84111 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
221760 |
Modular degree for the optimal curve |
Δ |
541367246073 = 3 · 237 · 53 |
Discriminant |
Eigenvalues |
1 3- 2 4 4 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-40480,-3137911] |
[a1,a2,a3,a4,a6] |
Generators |
[-536508910897259654082910823570117325321132523629719328:208076064815609314125088869727918115338119953966339197:4601703382215611343137331250393906538286514649923584] |
Generators of the group modulo torsion |
j |
49552182217/3657 |
j-invariant |
L |
13.874036031821 |
L(r)(E,1)/r! |
Ω |
0.33658335656522 |
Real period |
R |
82.440416344867 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000492 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3657a1 |
Quadratic twists by: -23 |