Properties

Label 243568.s
Number of curves 3
Conductor 243568
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("243568.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 243568.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
243568.s1 243568s3 [0, -1, 0, -60721128, 189144181616] [] 24074496  
243568.s2 243568s1 [0, -1, 0, -569608, -186665232] [] 2674944 \(\Gamma_0(N)\)-optimal
243568.s3 243568s2 [0, -1, 0, 3824392, 692697200] [] 8024832  

Rank

sage: E.rank()
 

The elliptic curves in class 243568.s have rank \(1\).

Modular form 243568.2.a.s

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{7} + q^{9} - 3q^{11} + q^{13} - 3q^{17} - 2q^{19} + O(q^{20}) \)

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.