Atkin-Lehner |
3+ 19+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
2679b |
Isogeny class |
Conductor |
2679 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1680 |
Modular degree for the optimal curve |
Δ |
112440309 = 3 · 192 · 473 |
Discriminant |
Eigenvalues |
-2 3+ -3 1 -5 -4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-132,332] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:23:1] [-8:28:1] |
Generators of the group modulo torsion |
j |
256289886208/112440309 |
j-invariant |
L |
1.7235048163105 |
L(r)(E,1)/r! |
Ω |
1.6864868713513 |
Real period |
R |
0.17032495633245 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000009 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42864e1 8037b1 66975g1 50901l1 |
Quadratic twists by: -4 -3 5 -19 |