Atkin-Lehner |
3- 11+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
1683i |
Isogeny class |
Conductor |
1683 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
512 |
Modular degree for the optimal curve |
Δ |
-11042163 = -1 · 310 · 11 · 17 |
Discriminant |
Eigenvalues |
2 3- 0 -3 11+ -4 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-75,-297] |
[a1,a2,a3,a4,a6] |
Generators |
[82:23:8] |
Generators of the group modulo torsion |
j |
-64000000/15147 |
j-invariant |
L |
4.847309013356 |
L(r)(E,1)/r! |
Ω |
0.80111725635371 |
Real period |
R |
3.0253430286963 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
26928bs1 107712cf1 561c1 42075y1 |
Quadratic twists by: -4 8 -3 5 |