Atkin-Lehner |
2- 3- 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
128832bp |
Isogeny class |
Conductor |
128832 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
-405270429696 = -1 · 226 · 32 · 11 · 61 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11- 2 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-129,30591] |
[a1,a2,a3,a4,a6] |
Generators |
[210:3051:1] |
Generators of the group modulo torsion |
j |
-912673/1545984 |
j-invariant |
L |
7.4537629802645 |
L(r)(E,1)/r! |
Ω |
0.76221478653312 |
Real period |
R |
4.8895423223733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000008758 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
128832e1 32208h1 |
Quadratic twists by: -4 8 |