Atkin-Lehner |
2+ 3+ 7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
81984r |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
49152 |
Modular degree for the optimal curve |
Δ |
14523219648 = 26 · 312 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- -4 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-812,7038] |
[a1,a2,a3,a4,a6] |
Generators |
[164610:2075241:1000] |
Generators of the group modulo torsion |
j |
926289116992/226925307 |
j-invariant |
L |
5.7163045684061 |
L(r)(E,1)/r! |
Ω |
1.1726358273318 |
Real period |
R |
9.749496702398 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004484 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81984z1 40992k3 |
Quadratic twists by: -4 8 |