Atkin-Lehner |
3- 11+ 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
68211b |
Isogeny class |
Conductor |
68211 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
16575273 = 37 · 11 · 13 · 53 |
Discriminant |
Eigenvalues |
1 3- 2 0 11+ 13- 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4266,108319] |
[a1,a2,a3,a4,a6] |
Generators |
[3601640:11638241:64000] |
Generators of the group modulo torsion |
j |
11779205551777/22737 |
j-invariant |
L |
9.1724654685916 |
L(r)(E,1)/r! |
Ω |
1.8865227415542 |
Real period |
R |
9.7242034423312 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998503 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22737c1 |
Quadratic twists by: -3 |