Atkin-Lehner |
2- 19+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
27968bq |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
41472 |
Modular degree for the optimal curve |
Δ |
7575076864 = 215 · 19 · 233 |
Discriminant |
Eigenvalues |
2- -3 -3 -2 5 -2 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1324,18064] |
[a1,a2,a3,a4,a6] |
Generators |
[-14:184:1] |
Generators of the group modulo torsion |
j |
7833173256/231173 |
j-invariant |
L |
2.3719798762121 |
L(r)(E,1)/r! |
Ω |
1.3134470168795 |
Real period |
R |
0.15049331046025 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27968bz1 13984l1 |
Quadratic twists by: -4 8 |