Atkin-Lehner |
2+ 3+ 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984d |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
170496 |
Modular degree for the optimal curve |
Δ |
-3085221888 = -1 · 214 · 32 · 73 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7+ 4 -4 5 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-13685,620781] |
[a1,a2,a3,a4,a6] |
Generators |
[68:3:1] |
Generators of the group modulo torsion |
j |
-17300948475904/188307 |
j-invariant |
L |
4.0972814215689 |
L(r)(E,1)/r! |
Ω |
1.2881286794896 |
Real period |
R |
1.5904006684929 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999893556 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984cp1 5124b1 |
Quadratic twists by: -4 8 |