Atkin-Lehner |
2+ 3+ 7+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
83664g |
Isogeny class |
Conductor |
83664 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
-1729083888 = -1 · 24 · 33 · 7 · 833 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ 0 3 -1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4191,104449] |
[a1,a2,a3,a4,a6] |
Generators |
[322:249:8] [56:213:1] |
Generators of the group modulo torsion |
j |
-18844861406976/4002509 |
j-invariant |
L |
9.8029314643499 |
L(r)(E,1)/r! |
Ω |
1.4509984424824 |
Real period |
R |
1.1259983904193 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999317 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
41832p1 83664b1 |
Quadratic twists by: -4 -3 |