Atkin-Lehner |
3+ 7- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
36309i |
Isogeny class |
Conductor |
36309 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
752640 |
Modular degree for the optimal curve |
Δ |
-1876307585184456879 = -1 · 3 · 79 · 138 · 19 |
Discriminant |
Eigenvalues |
-1 3+ 2 7- -2 13- 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3265067,2270434256] |
[a1,a2,a3,a4,a6] |
Generators |
[1000:2072:1] |
Generators of the group modulo torsion |
j |
-95393251687599559/46496651097 |
j-invariant |
L |
3.1799860057425 |
L(r)(E,1)/r! |
Ω |
0.25979696863049 |
Real period |
R |
3.0600684281519 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
108927t1 36309x1 |
Quadratic twists by: -3 -7 |