LMFDB - Elliptic curve isogeny class with LMFDB label 471900.eg (Cremona label 471900eg)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("eg1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 471900.eg have rank $0$.

The elliptic curves in class 471900.eg 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 LMFDB numbering.

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

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

The vertices are labelled with LMFDB labels.

sage:E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
471900.eg1	471900eg1	$[0, 1, 0, -587028273, 5474205772308]$	$6314146617344431898624/491941593$	$1743009080873346000$	$[2]$	$57093120$	$3.3929$	$\Gamma_0(N)$-optimal
471900.eg2	471900eg2	$[0, 1, 0, -586988948, 5474975913108]$	$-394554859317462604304/110153177479917$	$-6244578343983975693984000$	$[2]$	$114186240$	$3.7394$

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LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
471900.eg1	471900eg1	\([0, 1, 0, -587028273, 5474205772308]\)	\(6314146617344431898624/491941593\)	\(1743009080873346000\)	\([2]\)	\(57093120\)	\(3.3929\)	\(\Gamma_0(N)\)-optimal
471900.eg2	471900eg2	\([0, 1, 0, -586988948, 5474975913108]\)	\(-394554859317462604304/110153177479917\)	\(-6244578343983975693984000\)	\([2]\)	\(114186240\)	\(3.7394\)