Atkin-Lehner |
3- 7- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
83391r |
Isogeny class |
Conductor |
83391 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
76073189577 = 3 · 72 · 11 · 196 |
Discriminant |
Eigenvalues |
1 3- -2 7- 11+ -6 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-12282,-524729] |
[a1,a2,a3,a4,a6] |
Generators |
[511:11000:1] [67557:3342280:27] |
Generators of the group modulo torsion |
j |
4354703137/1617 |
j-invariant |
L |
13.833217376269 |
L(r)(E,1)/r! |
Ω |
0.45351974045437 |
Real period |
R |
30.501907948993 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999123 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
231a1 |
Quadratic twists by: -19 |