Atkin-Lehner |
3- 5+ 7+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
31605p |
Isogeny class |
Conductor |
31605 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
316800 |
Modular degree for the optimal curve |
Δ |
8711128125 = 33 · 55 · 74 · 43 |
Discriminant |
Eigenvalues |
0 3- 5+ 7+ 6 -4 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-1920571,1023816910] |
[a1,a2,a3,a4,a6] |
Generators |
[3141392:6543799:4096] |
Generators of the group modulo torsion |
j |
326304361537850343424/3628125 |
j-invariant |
L |
5.2518262732667 |
L(r)(E,1)/r! |
Ω |
0.65580486716949 |
Real period |
R |
8.0082148458795 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
94815ba1 31605l1 |
Quadratic twists by: -3 -7 |