Atkin-Lehner |
3- 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
25857p |
Isogeny class |
Conductor |
25857 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
41856 |
Modular degree for the optimal curve |
Δ |
-18051780123 = -1 · 37 · 134 · 172 |
Discriminant |
Eigenvalues |
-2 3- -4 -3 -4 13+ 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-507,7816] |
[a1,a2,a3,a4,a6] |
Generators |
[13:-59:1] [-206:489:8] |
Generators of the group modulo torsion |
j |
-692224/867 |
j-invariant |
L |
2.785311886011 |
L(r)(E,1)/r! |
Ω |
1.1091177577326 |
Real period |
R |
0.1046369162408 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000006 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8619f1 25857m1 |
Quadratic twists by: -3 13 |