Atkin-Lehner |
2- 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
27328ba |
Isogeny class |
Conductor |
27328 |
Conductor |
∏ cp |
7 |
Product of Tamagawa factors cp |
deg |
416640 |
Modular degree for the optimal curve |
Δ |
44515927776924352 = 26 · 77 · 615 |
Discriminant |
Eigenvalues |
2- 3 0 7- 1 -6 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-321235,-69338992] |
[a1,a2,a3,a4,a6] |
Generators |
[-222336:374948:729] |
Generators of the group modulo torsion |
j |
57281226796200168000/695561371514443 |
j-invariant |
L |
9.9039523220571 |
L(r)(E,1)/r! |
Ω |
0.20068398538987 |
Real period |
R |
7.0501406924613 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27328s1 13664g1 |
Quadratic twists by: -4 8 |