Atkin-Lehner |
2+ 3+ 5+ 53+ |
Signs for the Atkin-Lehner involutions |
Class |
84270b |
Isogeny class |
Conductor |
84270 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2426112 |
Modular degree for the optimal curve |
Δ |
6850915367529384000 = 26 · 36 · 53 · 537 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 2 0 -4 0 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-589948,-120910448] |
[a1,a2,a3,a4,a6] |
Generators |
[-213808:882188:343] |
Generators of the group modulo torsion |
j |
1024497361441/309096000 |
j-invariant |
L |
3.2043557067682 |
L(r)(E,1)/r! |
Ω |
0.17629085375131 |
Real period |
R |
4.5441320983597 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999939272 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
1590u1 |
Quadratic twists by: 53 |