Atkin-Lehner |
2+ 19- 23- |
Signs for the Atkin-Lehner involutions |
Class |
27968u |
Isogeny class |
Conductor |
27968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-8502272 = -1 · 210 · 192 · 23 |
Discriminant |
Eigenvalues |
2+ 3 0 -2 6 3 -8 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,20,-136] |
[a1,a2,a3,a4,a6] |
Generators |
[111:107:27] |
Generators of the group modulo torsion |
j |
864000/8303 |
j-invariant |
L |
9.8929597144521 |
L(r)(E,1)/r! |
Ω |
1.1476698643029 |
Real period |
R |
4.3100198158731 |
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 |
27968bj1 3496c1 |
Quadratic twists by: -4 8 |