Properties

Label 20286.ca
Number of curves $2$
Conductor $20286$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20286.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20286.ca1 20286co2 \([1, -1, 1, -267035, 49791179]\) \(24553362849625/1755162752\) \(150533500962724992\) \([2]\) \(258048\) \(2.0430\)  
20286.ca2 20286co1 \([1, -1, 1, 15205, 3390923]\) \(4533086375/60669952\) \(-5203426444296192\) \([2]\) \(129024\) \(1.6964\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20286.ca have rank \(1\).

Complex multiplication

The elliptic curves in class 20286.ca do not have complex multiplication.

Modular form 20286.2.a.ca

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{8} - 4q^{11} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.