Atkin-Lehner |
3- 5+ 29+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
69165g |
Isogeny class |
Conductor |
69165 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12800 |
Modular degree for the optimal curve |
Δ |
-84035475 = -1 · 37 · 52 · 29 · 53 |
Discriminant |
Eigenvalues |
0 3- 5+ -3 0 -5 -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-48,459] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:-23:1] [-62:149:8] |
Generators of the group modulo torsion |
j |
-16777216/115275 |
j-invariant |
L |
7.1374536844368 |
L(r)(E,1)/r! |
Ω |
1.6514733473037 |
Real period |
R |
1.0804675861336 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999099 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23055i1 |
Quadratic twists by: -3 |