Elliptic curve isogeny class with Cremona label 206310ce (LMFDB label 206310.n)

• Label: 206310ce
• Number of curves: $4$
• Conductor: $206310$
• CM: no
• Rank: $1$

Elliptic curves in class 206310ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206310.n3	206310ce1	\([1, 1, 0, -7152, -228816]\)	\(273359449/9360\)	\(1385615921040\)	\([2]\)	\(394240\)	\(1.1016\)	\(\Gamma_0(N)\)-optimal
206310.n2	206310ce2	\([1, 1, 0, -17732, 590076]\)	\(4165509529/1368900\)	\(202646328452100\)	\([2, 2]\)	\(788480\)	\(1.4482\)
206310.n1	206310ce3	\([1, 1, 0, -255782, 49675986]\)	\(12501706118329/2570490\)	\(380524772315610\)	\([2]\)	\(1576960\)	\(1.7948\)
206310.n4	206310ce4	\([1, 1, 0, 51038, 4124854]\)	\(99317171591/106616250\)	\(-15783031350596250\)	\([2]\)	\(1576960\)	\(1.7948\)

Rank

The elliptic curves in class 206310ce have rank \(1\).

Complex multiplication

The elliptic curves in class 206310ce do not have complex multiplication.

Modular form 206310.2.a.ce

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.