Atkin-Lehner |
3- 13+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
72111d |
Isogeny class |
Conductor |
72111 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
206976 |
Modular degree for the optimal curve |
Δ |
137812035831249 = 3 · 132 · 437 |
Discriminant |
Eigenvalues |
1 3- -2 -2 -2 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-12982,70235] |
[a1,a2,a3,a4,a6] |
Generators |
[14043:1657078:1] |
Generators of the group modulo torsion |
j |
38272753/21801 |
j-invariant |
L |
4.8518889856366 |
L(r)(E,1)/r! |
Ω |
0.49999733247307 |
Real period |
R |
4.8519148703765 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001004 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1677a1 |
Quadratic twists by: -43 |