LMFDB - Elliptic curve isogeny class with LMFDB label 3136.l (Cremona label 3136v)

Properties

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Show commands: SageMath

E = EllipticCurve("l1")

E.isogeny_class()

Elliptic curves in class 3136.l

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
3136.l1	3136v1	$[0, 0, 0, -7, 0]$	$1728$	$21952$	$[2]$	$256$	$-0.47748$	$\Gamma_0(N)$-optimal	$-4$
3136.l2	3136v2	$[0, 0, 0, 28, 0]$	$1728$	$-1404928$	$[2]$	$512$	$-0.13091$		$-4$

sage: E.rank()

The elliptic curves in class 3136.l have rank $1$.

Each elliptic curve in class 3136.l 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 LMFDB 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 LMFDB labels.

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LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
3136.l1	3136v1	\([0, 0, 0, -7, 0]\)	\(1728\)	\(21952\)	\([2]\)	\(256\)	\(-0.47748\)	\(\Gamma_0(N)\)-optimal	\(-4\)
3136.l2	3136v2	\([0, 0, 0, 28, 0]\)	\(1728\)	\(-1404928\)	\([2]\)	\(512\)	\(-0.13091\)		\(-4\)