Atkin-Lehner |
3- 7+ 17+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
13209f |
Isogeny class |
Conductor |
13209 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
7040 |
Modular degree for the optimal curve |
Δ |
-4419876699 = -1 · 310 · 7 · 172 · 37 |
Discriminant |
Eigenvalues |
0 3- -1 7+ -5 -5 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-371,4097] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:76:1] [7:43:1] |
Generators of the group modulo torsion |
j |
-5662595252224/4419876699 |
j-invariant |
L |
5.9634568962847 |
L(r)(E,1)/r! |
Ω |
1.2668065685863 |
Real period |
R |
0.23537361757365 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
39627e1 92463c1 |
Quadratic twists by: -3 -7 |