Atkin-Lehner |
3+ 11+ 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
128271c |
Isogeny class |
Conductor |
128271 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2945280 |
Modular degree for the optimal curve |
Δ |
-4229342725359609 = -1 · 34 · 112 · 138 · 232 |
Discriminant |
Eigenvalues |
1 3+ 3 4 11+ 13+ -5 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-3338936,2346947517] |
[a1,a2,a3,a4,a6] |
Generators |
[1068:225:1] |
Generators of the group modulo torsion |
j |
-5046629022322537/5184729 |
j-invariant |
L |
9.7062111323967 |
L(r)(E,1)/r! |
Ω |
0.36788297552245 |
Real period |
R |
3.2979954530039 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000090985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128271j1 |
Quadratic twists by: 13 |