Atkin-Lehner |
2- 3+ 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970bx |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
308 |
Product of Tamagawa factors cp |
deg |
97574400 |
Modular degree for the optimal curve |
Δ |
-8.6536544140591E+26 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 11- -1 5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-12030876030,-507925437602373] |
[a1,a2,a3,a4,a6] |
Generators |
[127501:5492039:1] |
Generators of the group modulo torsion |
j |
-7424865923464408587656521/33363583883827200 |
j-invariant |
L |
9.6110227535267 |
L(r)(E,1)/r! |
Ω |
0.007207673892709 |
Real period |
R |
4.3293605946919 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997271 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970k1 |
Quadratic twists by: -11 |