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

Properties

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Show commands: SageMath

E = EllipticCurve("c1")

E.isogeny_class()

Elliptic curves in class 2304c

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
2304.i2	2304c1	$[0, 0, 0, -30, -56]$	$8000$	$373248$	$[2]$	$192$	$-0.20124$	$\Gamma_0(N)$-optimal	$-8$
2304.i1	2304c2	$[0, 0, 0, -120, 448]$	$8000$	$23887872$	$[2]$	$384$	$0.14533$		$-8$

sage: E.rank()

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

Each elliptic curve in class 2304c 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.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
2304.i2	2304c1	\([0, 0, 0, -30, -56]\)	\(8000\)	\(373248\)	\([2]\)	\(192\)	\(-0.20124\)	\(\Gamma_0(N)\)-optimal	\(-8\)
2304.i1	2304c2	\([0, 0, 0, -120, 448]\)	\(8000\)	\(23887872\)	\([2]\)	\(384\)	\(0.14533\)		\(-8\)