Atkin-Lehner |
5+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
69575o |
Isogeny class |
Conductor |
69575 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-5000703125 = -1 · 57 · 112 · 232 |
Discriminant |
Eigenvalues |
-1 1 5+ -1 11- 2 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-1438,-21383] |
[a1,a2,a3,a4,a6] |
Generators |
[57:259:1] |
Generators of the group modulo torsion |
j |
-173945761/2645 |
j-invariant |
L |
3.6954927422739 |
L(r)(E,1)/r! |
Ω |
0.38728956360149 |
Real period |
R |
1.1927421656954 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999987655 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13915f1 69575m1 |
Quadratic twists by: 5 -11 |