Atkin-Lehner |
2+ 5+ 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
42160d |
Isogeny class |
Conductor |
42160 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
827904 |
Modular degree for the optimal curve |
Δ |
59867448305536000 = 210 · 53 · 17 · 317 |
Discriminant |
Eigenvalues |
2+ -3 5+ -4 4 -3 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-420883,-104435582] |
[a1,a2,a3,a4,a6] |
Generators |
[-357:566:1] |
Generators of the group modulo torsion |
j |
8052076803233381796/58464304985875 |
j-invariant |
L |
1.7822193713391 |
L(r)(E,1)/r! |
Ω |
0.18752072914906 |
Real period |
R |
4.7520596241089 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999646 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
21080c1 |
Quadratic twists by: -4 |