Atkin-Lehner |
2- 3- 5- 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160dp |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
320 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-18633240000000000 = -1 · 212 · 38 · 510 · 71 |
Discriminant |
Eigenvalues |
2- 3- 5- -2 2 -2 -4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-674905,213284903] |
[a1,a2,a3,a4,a6] |
Generators |
[551:3000:1] |
Generators of the group modulo torsion |
j |
-8300272382462293696/4549130859375 |
j-invariant |
L |
8.0803110243713 |
L(r)(E,1)/r! |
Ω |
0.38218860657015 |
Real period |
R |
0.26427760030526 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996306 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160ck1 34080g1 |
Quadratic twists by: -4 8 |