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Properties

Label 164730.u
Number of curves $2$
Conductor $164730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 164730.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.u1 164730cq2 \([1, 1, 0, -1895254347, -31741119233091]\) \(31191243455137987558006489/19767600000000000000\) \(477141808964400000000000000\) \([2]\) \(99090432\) \(4.0604\)  
164730.u2 164730cq1 \([1, 1, 0, -95963467, -690036800579]\) \(-4049001901026200674009/6177706475520000000\) \(-149114816314610810880000000\) \([2]\) \(49545216\) \(3.7138\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 164730.u have rank \(0\).

Complex multiplication

The elliptic curves in class 164730.u do not have complex multiplication.

Modular form 164730.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - q^{12} - q^{15} + q^{16} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.