Atkin-Lehner |
13+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
10309d |
Isogeny class |
Conductor |
10309 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
269568 |
Modular degree for the optimal curve |
Δ |
8409368002789 = 1310 · 61 |
Discriminant |
Eigenvalues |
-1 3 1 -2 2 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-7188447,7420034002] |
[a1,a2,a3,a4,a6] |
Generators |
[20263704:66761645:13824] |
Generators of the group modulo torsion |
j |
297985654937529/61 |
j-invariant |
L |
5.0458292374336 |
L(r)(E,1)/r! |
Ω |
0.42874533303102 |
Real period |
R |
11.768826034238 |
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 |
92781g1 10309b1 |
Quadratic twists by: -3 13 |