LMFDB - Elliptic curve isogeny class with Cremona label 479808rk (LMFDB label 479808.rk)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("rk1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 479808rk have rank $0$.

The elliptic curves in class 479808rk 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
479808.rk1	479808rk1	$[0, 0, 0, -527436, 147511952]$	$-19486825371/11662$	$-9711022565228544$	$[]$	$4423680$	$2.0117$	$\Gamma_0(N)$-optimal
479808.rk2	479808rk2	$[0, 0, 0, 460404, 610040592]$	$17779581/275128$	$-167014526127748153344$	$[]$	$13271040$	$2.5610$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
479808.rk1	479808rk1	\([0, 0, 0, -527436, 147511952]\)	\(-19486825371/11662\)	\(-9711022565228544\)	\([]\)	\(4423680\)	\(2.0117\)	\(\Gamma_0(N)\)-optimal
479808.rk2	479808rk2	\([0, 0, 0, 460404, 610040592]\)	\(17779581/275128\)	\(-167014526127748153344\)	\([]\)	\(13271040\)	\(2.5610\)