Atkin-Lehner |
2+ 5- 29+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68150h |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
846720 |
Modular degree for the optimal curve |
Δ |
32799232000000000 = 218 · 59 · 29 · 472 |
Discriminant |
Eigenvalues |
2+ 0 5- -4 -2 4 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-1002742,386636916] |
[a1,a2,a3,a4,a6] |
Generators |
[-31:20453:1] |
Generators of the group modulo torsion |
j |
57090196019543877/16793206784 |
j-invariant |
L |
3.125950072323 |
L(r)(E,1)/r! |
Ω |
0.36111666880312 |
Real period |
R |
4.3281719488897 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998167 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68150x1 |
Quadratic twists by: 5 |