Elliptic curve isogeny class with Cremona label 14112x (LMFDB label 14112.p)

• Label: 14112x
• Number of curves: $4$
• Conductor: $14112$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $1$

Elliptic curves in class 14112x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
14112.p3	14112x1	\([0, 0, 0, -441, 0]\)	\(1728\)	\(5489031744\)	\([2, 2]\)	\(6144\)	\(0.55830\)	\(\Gamma_0(N)\)-optimal	\(-4\)
14112.p1	14112x2	\([0, 0, 0, -4851, -129654]\)	\(287496\)	\(43912253952\)	\([2]\)	\(12288\)	\(0.90488\)		\(-16\)
14112.p2	14112x3	\([0, 0, 0, -4851, 129654]\)	\(287496\)	\(43912253952\)	\([2]\)	\(12288\)	\(0.90488\)		\(-16\)
14112.p4	14112x4	\([0, 0, 0, 1764, 0]\)	\(1728\)	\(-351298031616\)	\([2]\)	\(12288\)	\(0.90488\)		\(-4\)

Rank

The elliptic curves in class 14112x have rank \(1\).

Complex multiplication

Each elliptic curve in class 14112x has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 14112.2.a.x

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.