Atkin-Lehner |
2+ 3- 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
81984ba |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
2096640 |
Modular degree for the optimal curve |
Δ |
-4702174338613248 = -1 · 221 · 37 · 75 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 3 1 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2529665,1547772639] |
[a1,a2,a3,a4,a6] |
Generators |
[907:-576:1] |
Generators of the group modulo torsion |
j |
-6829249786786129249/17937371592 |
j-invariant |
L |
6.7794907440506 |
L(r)(E,1)/r! |
Ω |
0.37643323294588 |
Real period |
R |
0.64320747523327 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000303 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984ce1 2562i1 |
Quadratic twists by: -4 8 |