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

Properties

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Show commands: SageMath

sage:E = EllipticCurve("bci1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 705600.bci have rank $1$.

The elliptic curves in class 705600.bci 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.bci1	$[0, 0, 0, -179340, 29278480]$	$-30642435/56$	$-1165789023436800$	$[]$	$2654208$	$1.7826$
705600.bci2	$[0, 0, 0, 291060, 142989840]$	$179685/686$	$-10410787426546483200$	$[]$	$7962624$	$2.3319$

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height
705600.bci1	\([0, 0, 0, -179340, 29278480]\)	\(-30642435/56\)	\(-1165789023436800\)	\([]\)	\(2654208\)	\(1.7826\)
705600.bci2	\([0, 0, 0, 291060, 142989840]\)	\(179685/686\)	\(-10410787426546483200\)	\([]\)	\(7962624\)	\(2.3319\)