LMFDB - Elliptic curve isogeny class with Cremona label 462384cw (LMFDB label 462384.cw)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("cw1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 462384cw have rank $2$.

The elliptic curves in class 462384cw 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.

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

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
462384.cw1	462384cw1	$[0, 0, 0, -2535, 30758]$	$54000/19$	$633895172352$	$[2]$	$294912$	$0.96588$	$\Gamma_0(N)$-optimal
462384.cw2	462384cw2	$[0, 0, 0, 7605, 215306]$	$364500/361$	$-48176033098752$	$[2]$	$589824$	$1.3125$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
462384.cw1	462384cw1	\([0, 0, 0, -2535, 30758]\)	\(54000/19\)	\(633895172352\)	\([2]\)	\(294912\)	\(0.96588\)	\(\Gamma_0(N)\)-optimal
462384.cw2	462384cw2	\([0, 0, 0, 7605, 215306]\)	\(364500/361\)	\(-48176033098752\)	\([2]\)	\(589824\)	\(1.3125\)