LMFDB - Elliptic curve isogeny class with Cremona label 474320gx (LMFDB label 474320.gx)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("gx1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 474320gx have rank $0$.

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

sage:E.q_eigenform(10)

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.

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

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

The vertices are labelled with Cremona labels.

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474320.gx1	474320gx1	$[0, 1, 0, -476296, 128411380]$	$-1693700041/32000$	$-225771390107648000$	$[]$	$5225472$	$2.1245$	$\Gamma_0(N)$-optimal
474320.gx2	474320gx2	$[0, 1, 0, 1895304, 601782740]$	$106718863559/83886080$	$-591846152883792773120$	$[]$	$15676416$	$2.6738$

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LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474320.gx1	474320gx1	\([0, 1, 0, -476296, 128411380]\)	\(-1693700041/32000\)	\(-225771390107648000\)	\([]\)	\(5225472\)	\(2.1245\)	\(\Gamma_0(N)\)-optimal
474320.gx2	474320gx2	\([0, 1, 0, 1895304, 601782740]\)	\(106718863559/83886080\)	\(-591846152883792773120\)	\([]\)	\(15676416\)	\(2.6738\)