LMFDB - Elliptic curve isogeny class with Cremona label 486720nq (LMFDB label 486720.nq)

Properties

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Show commands: SageMath

sage:E = EllipticCurve("nq1") E.isogeny_class()

Rank

sage:E.rank()

The elliptic curves in class 486720nq have rank $2$.

The elliptic curves in class 486720nq 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
486720.nq1	486720nq1	$[0, 0, 0, -28392, 1849874]$	$-303464448/1625$	$-13553679672000$	$[]$	$1161216$	$1.3643$	$\Gamma_0(N)$-optimal
486720.nq2	486720nq2	$[0, 0, 0, 73008, 9846954]$	$7077888/10985$	$-66793075570802880$	$[]$	$3483648$	$1.9136$

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LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
486720.nq1	486720nq1	\([0, 0, 0, -28392, 1849874]\)	\(-303464448/1625\)	\(-13553679672000\)	\([]\)	\(1161216\)	\(1.3643\)	\(\Gamma_0(N)\)-optimal
486720.nq2	486720nq2	\([0, 0, 0, 73008, 9846954]\)	\(7077888/10985\)	\(-66793075570802880\)	\([]\)	\(3483648\)	\(1.9136\)