LMFDB - Elliptic curve isogeny class with Cremona label 12544d (LMFDB label 12544.n)

Properties

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Show commands: SageMath

E = EllipticCurve("d1")

E.isogeny_class()

Elliptic curves in class 12544d

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
12544.n2	12544d1	$[0, -1, 0, -163, -657]$	$8000$	$60236288$	$[2]$	$3072$	$0.22241$	$\Gamma_0(N)$-optimal	$-8$
12544.n1	12544d2	$[0, -1, 0, -653, 5909]$	$8000$	$3855122432$	$[2]$	$6144$	$0.56898$		$-8$

sage: E.rank()

The elliptic curves in class 12544d have rank $0$.

Each elliptic curve in class 12544d has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-2}) $.

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.

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Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
12544.n2	12544d1	\([0, -1, 0, -163, -657]\)	\(8000\)	\(60236288\)	\([2]\)	\(3072\)	\(0.22241\)	\(\Gamma_0(N)\)-optimal	\(-8\)
12544.n1	12544d2	\([0, -1, 0, -653, 5909]\)	\(8000\)	\(3855122432\)	\([2]\)	\(6144\)	\(0.56898\)		\(-8\)