LMFDB - Elliptic curve isogeny class with Cremona label 2304i (LMFDB label 2304.n)

Properties

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Show commands: SageMath

E = EllipticCurve("i1")

E.isogeny_class()

Elliptic curves in class 2304i

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
2304.n2	2304i1	$[0, 0, 0, 6, 0]$	$1728$	$-13824$	$[2]$	$128$	$-0.51602$	$\Gamma_0(N)$-optimal	$-4$
2304.n1	2304i2	$[0, 0, 0, -24, 0]$	$1728$	$884736$	$[2]$	$256$	$-0.16945$		$-4$

sage: E.rank()

The elliptic curves in class 2304i have rank $0$.

Each elliptic curve in class 2304i has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-1}) $.

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
2304.n2	2304i1	\([0, 0, 0, 6, 0]\)	\(1728\)	\(-13824\)	\([2]\)	\(128\)	\(-0.51602\)	\(\Gamma_0(N)\)-optimal	\(-4\)
2304.n1	2304i2	\([0, 0, 0, -24, 0]\)	\(1728\)	\(884736\)	\([2]\)	\(256\)	\(-0.16945\)		\(-4\)