Elliptic curve isogeny class with Cremona label 56784b (LMFDB label 56784.g)

• Label: 56784b
• Number of curves: $4$
• Conductor: $56784$
• CM: no
• Rank: $1$

Elliptic curves in class 56784b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
56784.g3	56784b1	\([0, -1, 0, -1239, 17094]\)	\(2725888/21\)	\(1621807824\)	\([2]\)	\(36864\)	\(0.59629\)	\(\Gamma_0(N)\)-optimal
56784.g2	56784b2	\([0, -1, 0, -2084, -8256]\)	\(810448/441\)	\(544927428864\)	\([2, 2]\)	\(73728\)	\(0.94286\)
56784.g4	56784b3	\([0, -1, 0, 8056, -73152]\)	\(11696828/7203\)	\(-35601925352448\)	\([2]\)	\(147456\)	\(1.2894\)
56784.g1	56784b4	\([0, -1, 0, -25744, -1579280]\)	\(381775972/567\)	\(2802483919872\)	\([2]\)	\(147456\)	\(1.2894\)

Rank

The elliptic curves in class 56784b have rank \(1\).

Complex multiplication

The elliptic curves in class 56784b do not have complex multiplication.

Modular form 56784.2.a.b

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.