LMFDB - Elliptic curve isogeny class with LMFDB label 705600.bba

Properties

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Show commands: SageMath

sage:E = EllipticCurve("bba1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 705600.bba have rank $0$.

The elliptic curves in class 705600.bba 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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

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
705600.bba1	$[0, 0, 0, -40351500, -98814870000]$	$-30642435/56$	$-13279065595084800000000$	$[]$	$39813120$	$3.1366$
705600.bba2	$[0, 0, 0, 808500, -661990000]$	$179685/686$	$-223139305267200000000$	$[]$	$13271040$	$2.5873$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
705600.bba1	\([0, 0, 0, -40351500, -98814870000]\)	\(-30642435/56\)	\(-13279065595084800000000\)	\([]\)	\(39813120\)	\(3.1366\)
705600.bba2	\([0, 0, 0, 808500, -661990000]\)	\(179685/686\)	\(-223139305267200000000\)	\([]\)	\(13271040\)	\(2.5873\)