Atkin-Lehner |
2+ 3+ 5- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68970k |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8870400 |
Modular degree for the optimal curve |
Δ |
-4.8847623164311E+20 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -1 11- 1 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-99428727,381566704149] |
[a1,a2,a3,a4,a6] |
Generators |
[6285:67368:1] |
Generators of the group modulo torsion |
j |
-7424865923464408587656521/33363583883827200 |
j-invariant |
L |
3.4312727977862 |
L(r)(E,1)/r! |
Ω |
0.14625456025822 |
Real period |
R |
5.8652407008719 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992059 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68970bx1 |
Quadratic twists by: -11 |