Atkin-Lehner |
2- 3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
27744s |
Isogeny class |
Conductor |
27744 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-55488 = -1 · 26 · 3 · 172 |
Discriminant |
Eigenvalues |
2- 3+ -2 -3 2 -5 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,6,-12] |
[a1,a2,a3,a4,a6] |
Generators |
[2:2:1] [7:18:1] |
Generators of the group modulo torsion |
j |
1088/3 |
j-invariant |
L |
5.8969822892213 |
L(r)(E,1)/r! |
Ω |
1.8164764570172 |
Real period |
R |
1.6231926008292 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27744ba1 55488dt1 83232l1 27744bc1 |
Quadratic twists by: -4 8 -3 17 |