Atkin-Lehner |
2- 3+ 17+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
67728p |
Isogeny class |
Conductor |
67728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7872 |
Modular degree for the optimal curve |
Δ |
-3454128 = -1 · 24 · 32 · 172 · 83 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 0 2 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,11,-92] |
[a1,a2,a3,a4,a6] |
Generators |
[52:372:1] |
Generators of the group modulo torsion |
j |
8388608/215883 |
j-invariant |
L |
4.1770962349567 |
L(r)(E,1)/r! |
Ω |
1.2117441667753 |
Real period |
R |
3.4471766814942 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983541 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16932e1 |
Quadratic twists by: -4 |