Properties

Label 221760ls
Number of curves $4$
Conductor $221760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ls1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760ls

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.cv4 221760ls1 \([0, 0, 0, 13092, -552368]\) \(20777545136/23059575\) \(-275422087987200\) \([2]\) \(524288\) \(1.4573\) \(\Gamma_0(N)\)-optimal
221760.cv3 221760ls2 \([0, 0, 0, -74028, -5187152]\) \(939083699236/300155625\) \(14340158300160000\) \([2, 2]\) \(1048576\) \(1.8039\)  
221760.cv2 221760ls3 \([0, 0, 0, -470028, 120107248]\) \(120186986927618/4332064275\) \(413935187587891200\) \([2]\) \(2097152\) \(2.1504\)  
221760.cv1 221760ls4 \([0, 0, 0, -1071948, -427107728]\) \(1425631925916578/270703125\) \(25866086400000000\) \([2]\) \(2097152\) \(2.1504\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760ls have rank \(1\).

Complex multiplication

The elliptic curves in class 221760ls do not have complex multiplication.

Modular form 221760.2.a.ls

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} + 2 q^{13} + 2 q^{17} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.