LMFDB - Elliptic curve isogeny class with Cremona label 43264f (LMFDB label 43264.c)

Properties

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Show commands: SageMath

E = EllipticCurve("f1")

E.isogeny_class()

Elliptic curves in class 43264f

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
43264.c2	43264f1	$[0, 1, 0, -563, 4369]$	$8000$	$2471326208$	$[2]$	$18816$	$0.53193$	$\Gamma_0(N)$-optimal	$-8$
43264.c1	43264f2	$[0, 1, 0, -2253, -37205]$	$8000$	$158164877312$	$[2]$	$37632$	$0.87850$		$-8$

sage: E.rank()

The elliptic curves in class 43264f have rank $1$.

Each elliptic curve in class 43264f 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
43264.c2	43264f1	\([0, 1, 0, -563, 4369]\)	\(8000\)	\(2471326208\)	\([2]\)	\(18816\)	\(0.53193\)	\(\Gamma_0(N)\)-optimal	\(-8\)
43264.c1	43264f2	\([0, 1, 0, -2253, -37205]\)	\(8000\)	\(158164877312\)	\([2]\)	\(37632\)	\(0.87850\)		\(-8\)