Atkin-Lehner |
3- 5+ 19- 59- |
Signs for the Atkin-Lehner involutions |
Class |
84075o |
Isogeny class |
Conductor |
84075 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
290304 |
Modular degree for the optimal curve |
Δ |
-32752204453125 = -1 · 39 · 57 · 192 · 59 |
Discriminant |
Eigenvalues |
-1 3- 5+ -5 -2 -3 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-8338,401417] |
[a1,a2,a3,a4,a6] |
Generators |
[272:4139:1] [47:-361:1] |
Generators of the group modulo torsion |
j |
-4102915888729/2096141085 |
j-invariant |
L |
6.7455882383464 |
L(r)(E,1)/r! |
Ω |
0.61140182246548 |
Real period |
R |
0.15323592781591 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998667 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16815b1 |
Quadratic twists by: 5 |