LMFDB - Elliptic curve isogeny class with LMFDB label 7744.bb (Cremona label 7744a)

Properties

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Show commands: SageMath

E = EllipticCurve("bb1")

E.isogeny_class()

Elliptic curves in class 7744.bb

sage: E.isogeny_class().curves

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7744.bb1	7744a2	$[0, 1, 0, -3549, -84691]$	$-32768$	$-150908652224$	$[]$	$6336$	$0.92245$		$-11$
7744.bb2	7744a1	$[0, 1, 0, -29, 53]$	$-32768$	$-85184$	$[]$	$576$	$-0.27650$	$\Gamma_0(N)$-optimal	$-11$

sage: E.rank()

The elliptic curves in class 7744.bb have rank $1$.

Each elliptic curve in class 7744.bb has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-11}) $.

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.

$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$

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
7744.bb1	7744a2	\([0, 1, 0, -3549, -84691]\)	\(-32768\)	\(-150908652224\)	\([]\)	\(6336\)	\(0.92245\)		\(-11\)
7744.bb2	7744a1	\([0, 1, 0, -29, 53]\)	\(-32768\)	\(-85184\)	\([]\)	\(576\)	\(-0.27650\)	\(\Gamma_0(N)\)-optimal	\(-11\)