Atkin-Lehner |
2+ 3- 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
84474y |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
112 |
Product of Tamagawa factors cp |
deg |
15966720 |
Modular degree for the optimal curve |
Δ |
-2.2609966433565E+24 |
Discriminant |
Eigenvalues |
2+ 3- 0 -3 3 13- 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-42872247,130041216477] |
[a1,a2,a3,a4,a6] |
Generators |
[5781:-277431:1] [81:355725:1] |
Generators of the group modulo torsion |
j |
-254099214331341625/65925097924608 |
j-invariant |
L |
8.1675859354055 |
L(r)(E,1)/r! |
Ω |
0.078044604267089 |
Real period |
R |
0.93439995129128 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996637 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28158t1 4446p1 |
Quadratic twists by: -3 -19 |