Atkin-Lehner |
2- 19- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
27968bt |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
127088700763930624 = 239 · 19 · 233 |
Discriminant |
Eigenvalues |
2- 1 -3 -2 -3 -2 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-507457,137908159] |
[a1,a2,a3,a4,a6] |
Generators |
[261:4828:1] |
Generators of the group modulo torsion |
j |
55129288688387857/484804919296 |
j-invariant |
L |
3.5278027156316 |
L(r)(E,1)/r! |
Ω |
0.33140694495152 |
Real period |
R |
5.3224634688143 |
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 |
27968f1 6992j1 |
Quadratic twists by: -4 8 |