Atkin-Lehner |
7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
17689b |
Isogeny class |
Conductor |
17689 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
26880 |
Modular degree for the optimal curve |
Δ |
-39540770059 = -1 · 78 · 193 |
Discriminant |
Eigenvalues |
-2 2 2 7+ 5 2 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-2172,-39404] |
[a1,a2,a3,a4,a6] |
Generators |
[527:12037:1] |
Generators of the group modulo torsion |
j |
-28672 |
j-invariant |
L |
4.4082412518967 |
L(r)(E,1)/r! |
Ω |
0.34893822424617 |
Real period |
R |
6.3166499763963 |
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 |
17689f1 17689a1 |
Quadratic twists by: -7 -19 |