Atkin-Lehner |
2+ 3- 13- 73- |
Signs for the Atkin-Lehner involutions |
Class |
68328d |
Isogeny class |
Conductor |
68328 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-113617862452224 = -1 · 210 · 36 · 134 · 732 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 -6 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36819,2767230] |
[a1,a2,a3,a4,a6] |
Generators |
[-105:2340:1] [70:730:1] |
Generators of the group modulo torsion |
j |
-7394557561668/152201569 |
j-invariant |
L |
10.780623357609 |
L(r)(E,1)/r! |
Ω |
0.59203016165801 |
Real period |
R |
2.276198084114 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999809 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7592c2 |
Quadratic twists by: -3 |