Atkin-Lehner |
3+ 5+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
6825d |
Isogeny class |
Conductor |
6825 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
21946640625 = 32 · 57 · 74 · 13 |
Discriminant |
Eigenvalues |
-1 3+ 5+ 7- 4 13- -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-713,1406] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:85:1] |
Generators of the group modulo torsion |
j |
2565726409/1404585 |
j-invariant |
L |
2.4188084802488 |
L(r)(E,1)/r! |
Ω |
1.0504876293787 |
Real period |
R |
1.1512788978198 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
109200ft1 20475ba1 1365c1 47775cj1 |
Quadratic twists by: -4 -3 5 -7 |