Atkin-Lehner |
5+ 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
13175d |
Isogeny class |
Conductor |
13175 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
221760 |
Modular degree for the optimal curve |
Δ |
-36540190616171875 = -1 · 57 · 17 · 317 |
Discriminant |
Eigenvalues |
-1 -2 5+ -5 -5 5 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-185088,31983667] |
[a1,a2,a3,a4,a6] |
Generators |
[-63:6619:1] [122:3289:1] |
Generators of the group modulo torsion |
j |
-44878529736708409/2338572199435 |
j-invariant |
L |
2.6791530036011 |
L(r)(E,1)/r! |
Ω |
0.36156198607872 |
Real period |
R |
0.26464075186824 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
118575p1 2635c1 |
Quadratic twists by: -3 5 |