Elliptic curve isogeny class with LMFDB label 7056.bb (Cremona label 7056bf)

• Label: 7056.bb
• Number of curves: $4$
• Conductor: $7056$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $1$

Elliptic curves in class 7056.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
7056.bb1	7056bf4	\([0, 0, 0, -6615, -203742]\)	\(54000\)	\(592815428352\)	\([2]\)	\(6912\)	\(1.0534\)		\(-12\)
7056.bb2	7056bf2	\([0, 0, 0, -735, 7546]\)	\(54000\)	\(813189888\)	\([2]\)	\(2304\)	\(0.50411\)		\(-12\)
7056.bb3	7056bf3	\([0, 0, 0, 0, -9261]\)	\(0\)	\(-37050964272\)	\([2]\)	\(3456\)	\(0.70685\)		\(-3\)
7056.bb4	7056bf1	\([0, 0, 0, 0, 343]\)	\(0\)	\(-50824368\)	\([2]\)	\(1152\)	\(0.15754\)	\(\Gamma_0(N)\)-optimal	\(-3\)

Rank

The elliptic curves in class 7056.bb have rank \(1\).

Complex multiplication

Each elliptic curve in class 7056.bb has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 7056.2.a.bb

Isogeny 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.