Atkin-Lehner |
2+ 3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
27744b |
Isogeny class |
Conductor |
27744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-118033833938006016 = -1 · 212 · 35 · 179 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -2 5 -5 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-63965,-17642187] |
[a1,a2,a3,a4,a6] |
Generators |
[1120171:19898228:2197] |
Generators of the group modulo torsion |
j |
-292754944/1193859 |
j-invariant |
L |
4.2732258744471 |
L(r)(E,1)/r! |
Ω |
0.13684542037189 |
Real period |
R |
7.806665840249 |
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 |
27744w1 55488bi1 83232bg1 1632d1 |
Quadratic twists by: -4 8 -3 17 |