Atkin-Lehner |
2+ 7- 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614f |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1330560 |
Modular degree for the optimal curve |
Δ |
-6264843678993815552 = -1 · 211 · 73 · 139 · 292 |
Discriminant |
Eigenvalues |
2+ -1 2 7- -3 13+ -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,435341,-47555347] |
[a1,a2,a3,a4,a6] |
Generators |
[109:1044:1] [499:-17403:1] |
Generators of the group modulo torsion |
j |
1890387126561023/1297926576128 |
j-invariant |
L |
7.321293573084 |
L(r)(E,1)/r! |
Ω |
0.13492037449556 |
Real period |
R |
2.2609920852957 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999643 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5278d1 |
Quadratic twists by: 13 |