Atkin-Lehner |
2- 3+ 7- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
128772b |
Isogeny class |
Conductor |
128772 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-13271309796528 = -1 · 24 · 33 · 78 · 732 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 6 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1176,-175959] |
[a1,a2,a3,a4,a6] |
Generators |
[91:686:1] |
Generators of the group modulo torsion |
j |
-3538944/261121 |
j-invariant |
L |
7.3166183455126 |
L(r)(E,1)/r! |
Ω |
0.31213879677997 |
Real period |
R |
1.9533560145953 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999898429 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128772a1 18396a1 |
Quadratic twists by: -3 -7 |