LMFDB - Elliptic curve isogeny class with LMFDB label 1411200.eo

Properties

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Show commands: SageMath

sage:E = EllipticCurve("eo1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 1411200.eo have rank $0$.

The elliptic curves in class 1411200.eo 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	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
1411200.eo1	$[0, 0, 0, -3221343300, -70323600382000]$	$336751085874643808/271318359375$	$2978550174678750000000000000$	$[2]$	$1132462080$	$4.2014$
1411200.eo2	$[0, 0, 0, -158267550, -1582054400500]$	$-1277978627383936/2412172153125$	$-827530595030997112500000000$	$[2]$	$566231040$	$3.8549$

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LMFDB label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
1411200.eo1	\([0, 0, 0, -3221343300, -70323600382000]\)	\(336751085874643808/271318359375\)	\(2978550174678750000000000000\)	\([2]\)	\(1132462080\)	\(4.2014\)
1411200.eo2	\([0, 0, 0, -158267550, -1582054400500]\)	\(-1277978627383936/2412172153125\)	\(-827530595030997112500000000\)	\([2]\)	\(566231040\)	\(3.8549\)