Properties

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

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 221760.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.cu1 221760lr4 \([0, 0, 0, -15001068, -22361378128]\) \(1953542217204454969/170843779260\) \(32648754647673077760\) \([2]\) \(7864320\) \(2.7857\)  
221760.cu2 221760lr3 \([0, 0, 0, -5439468, 4633345712]\) \(93137706732176569/5369647977540\) \(1026155708580275159040\) \([2]\) \(7864320\) \(2.7857\)  
221760.cu3 221760lr2 \([0, 0, 0, -1004268, -296822608]\) \(586145095611769/140040608400\) \(26762177026090598400\) \([2, 2]\) \(3932160\) \(2.4391\)  
221760.cu4 221760lr1 \([0, 0, 0, 147732, -29097808]\) \(1865864036231/2993760000\) \(-572116445429760000\) \([2]\) \(1966080\) \(2.0925\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 221760.2.a.cu

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.