Atkin-Lehner |
2+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
80344a |
Isogeny class |
Conductor |
80344 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
230208 |
Modular degree for the optimal curve |
Δ |
50101672538368 = 28 · 119 · 83 |
Discriminant |
Eigenvalues |
2+ 0 2 4 11+ 2 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-38599,-2898918] |
[a1,a2,a3,a4,a6] |
Generators |
[-18109506123160335:22591032410437064:160235725705875] |
Generators of the group modulo torsion |
j |
10536048/83 |
j-invariant |
L |
8.6522657712522 |
L(r)(E,1)/r! |
Ω |
0.34077038712087 |
Real period |
R |
25.39031001144 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994625 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
80344e1 |
Quadratic twists by: -11 |