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Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 28566r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28566.d2 28566r1 \([1, -1, 0, -1686, -26574]\) \(-132651/2\) \(-7993938006\) \([]\) \(23760\) \(0.70324\) \(\Gamma_0(N)\)-optimal
28566.d3 28566r2 \([1, -1, 0, 6249, -135019]\) \(9261/8\) \(-23310323225496\) \([]\) \(71280\) \(1.2525\)  
28566.d1 28566r3 \([1, -1, 0, -65166, 8506196]\) \(-1167051/512\) \(-13426746177885696\) \([]\) \(213840\) \(1.8018\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28566.2.a.r

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.