Properties

Label 28566.bl
Number of curves $3$
Conductor $28566$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 28566.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28566.bl1 28566bc3 \([1, -1, 1, -15176, 732673]\) \(-132651/2\) \(-5827580806374\) \([]\) \(71280\) \(1.2525\)  
28566.bl2 28566bc2 \([1, -1, 1, -7241, -312631]\) \(-1167051/512\) \(-18418033165824\) \([]\) \(71280\) \(1.2525\)  
28566.bl3 28566bc1 \([1, -1, 1, 694, 4769]\) \(9261/8\) \(-31975752024\) \([]\) \(23760\) \(0.70324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28566.bl have rank \(1\).

Complex multiplication

The elliptic curves in class 28566.bl do not have complex multiplication.

Modular form 28566.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} + q^{7} + q^{8} + 3 q^{10} - 3 q^{11} - 4 q^{13} + q^{14} + q^{16} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.