Atkin-Lehner |
2- 3+ 7+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
127512w |
Isogeny class |
Conductor |
127512 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
-1219814920025856 = -1 · 28 · 33 · 78 · 113 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 11+ 2 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,21009,-1204110] |
[a1,a2,a3,a4,a6] |
Generators |
[243:4272:1] |
Generators of the group modulo torsion |
j |
148366593659664/176477853013 |
j-invariant |
L |
4.7671514037913 |
L(r)(E,1)/r! |
Ω |
0.26086834421153 |
Real period |
R |
4.5685414433119 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000076937 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127512b1 |
Quadratic twists by: -3 |