LMFDB - Elliptic curve isogeny class with Cremona label 485100ia (LMFDB label 485100.ia)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("ia1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 485100ia have rank $0$.

The elliptic curves in class 485100ia 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
485100.ia1	485100ia1	$[0, 0, 0, -60729375, 182159153750]$	$-2888047810000/35937$	$-308217709037700000000$	$[]$	$39191040$	$3.0786$	$\Gamma_0(N)$-optimal
485100.ia2	485100ia2	$[0, 0, 0, -27654375, 378909098750]$	$-272709010000/7073843073$	$-60669608093392983300000000$	$[]$	$117573120$	$3.6279$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485100.ia1	485100ia1	\([0, 0, 0, -60729375, 182159153750]\)	\(-2888047810000/35937\)	\(-308217709037700000000\)	\([]\)	\(39191040\)	\(3.0786\)	\(\Gamma_0(N)\)-optimal
485100.ia2	485100ia2	\([0, 0, 0, -27654375, 378909098750]\)	\(-272709010000/7073843073\)	\(-60669608093392983300000000\)	\([]\)	\(117573120\)	\(3.6279\)