Properties

Label 221760.cl
Number of curves $4$
Conductor $221760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221760.cl1 221760es4 \([0, 0, 0, -1785468, 484166608]\) \(52702650535889104/22020583921875\) \(263012445045504000000\) \([2]\) \(7962624\) \(2.6153\)  
221760.cl2 221760es2 \([0, 0, 0, -1539228, 735025552]\) \(33766427105425744/9823275\) \(117328567910400\) \([2]\) \(2654208\) \(2.0660\)  
221760.cl3 221760es1 \([0, 0, 0, -95808, 11583448]\) \(-130287139815424/2250652635\) \(-1680103189416960\) \([2]\) \(1327104\) \(1.7194\) \(\Gamma_0(N)\)-optimal
221760.cl4 221760es3 \([0, 0, 0, 370752, 55510072]\) \(7549996227362816/6152409907875\) \(-4592749386589056000\) \([2]\) \(3981312\) \(2.2687\)  

Rank

sage: E.rank()
 

The elliptic curves in class 221760.cl have rank \(0\).

Complex multiplication

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

Modular form 221760.2.a.cl

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} + q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.