Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
27968bx |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
492800 |
Modular degree for the optimal curve |
Δ |
-3943894205258102464 = -1 · 26 · 1911 · 232 |
Discriminant |
Eigenvalues |
2- -2 -1 -1 1 -6 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-911011,-348358497] |
[a1,a2,a3,a4,a6] |
Generators |
[2174:89167:1] |
Generators of the group modulo torsion |
j |
-1306517037693189331456/61623346957157851 |
j-invariant |
L |
2.5220054561265 |
L(r)(E,1)/r! |
Ω |
0.077053914230478 |
Real period |
R |
1.4877454674038 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27968bo1 13984a1 |
Quadratic twists by: -4 8 |