Properties

Label 474320hu
Number of curves $2$
Conductor $474320$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("hu1")
 
E.isogeny_class()
 

Elliptic curves in class 474320hu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
474320.hu2 474320hu1 \([0, 1, 0, 180, 6488]\) \(176/5\) \(-18221477120\) \([]\) \(217728\) \(0.64890\) \(\Gamma_0(N)\)-optimal*
474320.hu1 474320hu2 \([0, 1, 0, -21380, 1196600]\) \(-296587984/125\) \(-455536928000\) \([]\) \(653184\) \(1.1982\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 474320hu1.

Rank

sage: E.rank()
 

The elliptic curves in class 474320hu have rank \(1\).

Complex multiplication

The elliptic curves in class 474320hu do not have complex multiplication.

Modular form 474320.2.a.hu

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2 q^{9} + 2 q^{13} + q^{15} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.