Atkin-Lehner |
2- 13+ 17- 19- |
Signs for the Atkin-Lehner involutions |
Class |
67184r |
Isogeny class |
Conductor |
67184 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
7091331749445632 = 216 · 132 · 173 · 194 |
Discriminant |
Eigenvalues |
2- -2 -2 -2 -6 13+ 17- 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-269064,53476852] |
[a1,a2,a3,a4,a6] |
Generators |
[-436:9386:1] [-322:10336:1] |
Generators of the group modulo torsion |
j |
525935106358018057/1731282165392 |
j-invariant |
L |
5.2733200491193 |
L(r)(E,1)/r! |
Ω |
0.42116918920401 |
Real period |
R |
0.52169454544043 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999909 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8398b1 |
Quadratic twists by: -4 |