LMFDB - Elliptic curve isogeny class with Cremona label 478800ce (LMFDB label 478800.ce)

Properties

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Show commands: SageMath

sage:E = EllipticCurve([0, 0, 0, -1551675, 743886250]) E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 478800ce have rank $2$.

The elliptic curves in class 478800ce 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
478800.ce2	478800ce1	$[0, 0, 0, -1551675, 743886250]$	$8855610342769/1008273$	$47041985088000000$	$[2]$	$6881280$	$2.2266$	$\Gamma_0(N)$-optimal
478800.ce1	478800ce2	$[0, 0, 0, -1677675, 615996250]$	$11192824869409/2963890503$	$138283275307968000000$	$[2]$	$13762560$	$2.5732$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
478800.ce2	478800ce1	\([0, 0, 0, -1551675, 743886250]\)	\(8855610342769/1008273\)	\(47041985088000000\)	\([2]\)	\(6881280\)	\(2.2266\)	\(\Gamma_0(N)\)-optimal
478800.ce1	478800ce2	\([0, 0, 0, -1677675, 615996250]\)	\(11192824869409/2963890503\)	\(138283275307968000000\)	\([2]\)	\(13762560\)	\(2.5732\)