Atkin-Lehner |
2+ 3+ 17+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
27336b |
Isogeny class |
Conductor |
27336 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
157440 |
Modular degree for the optimal curve |
Δ |
-6158744874480384 = -1 · 28 · 35 · 173 · 674 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -4 3 -1 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2559,-3776283] |
[a1,a2,a3,a4,a6] |
Generators |
[437:8978:1] [169:1206:1] |
Generators of the group modulo torsion |
j |
7236438588416/24057597165939 |
j-invariant |
L |
6.223709085093 |
L(r)(E,1)/r! |
Ω |
0.19673010907976 |
Real period |
R |
1.9772358163063 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54672d1 82008r1 |
Quadratic twists by: -4 -3 |