Atkin-Lehner |
3- 5- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
8415p |
Isogeny class |
Conductor |
8415 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-17950416226875 = -1 · 312 · 54 · 11 · 173 |
Discriminant |
Eigenvalues |
0 3- 5- -1 11- 2 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-16842,-865620] |
[a1,a2,a3,a4,a6] |
j |
-724731558068224/24623341875 |
j-invariant |
L |
1.6729934762404 |
L(r)(E,1)/r! |
Ω |
0.20912418453005 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2805c1 42075bi1 92565bu1 |
Quadratic twists by: -3 5 -11 |