Atkin-Lehner |
2+ 3+ 5- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
27840x |
Isogeny class |
Conductor |
27840 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
2138112000 = 216 · 32 · 53 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 2 -4 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4865,132225] |
[a1,a2,a3,a4,a6] |
Generators |
[35:60:1] [-55:480:1] |
Generators of the group modulo torsion |
j |
194348673796/32625 |
j-invariant |
L |
7.1790216050688 |
L(r)(E,1)/r! |
Ω |
1.4192843469825 |
Real period |
R |
0.84303304224327 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27840dz1 3480h1 83520br1 |
Quadratic twists by: -4 8 -3 |