Atkin-Lehner |
13+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
10309b |
Isogeny class |
Conductor |
10309 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
1742221 = 134 · 61 |
Discriminant |
Eigenvalues |
1 3 -1 2 -2 13+ 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-42535,3387164] |
[a1,a2,a3,a4,a6] |
Generators |
[206076:-100879:1728] |
Generators of the group modulo torsion |
j |
297985654937529/61 |
j-invariant |
L |
8.7543141554018 |
L(r)(E,1)/r! |
Ω |
1.5458632823592 |
Real period |
R |
5.6630584705015 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
92781i1 10309d1 |
Quadratic twists by: -3 13 |