Elliptic curve isogeny class with LMFDB label 140679.o (Cremona label 140679i)

• Label: 140679.o
• Number of curves: $4$
• Conductor: $140679$
• CM: no
• Rank: $1$

Elliptic curves in class 140679.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
140679.o1	140679i3	\([1, -1, 1, -5258714, 4642886000]\)	\(187519537050946633/1186707753\)	\(101779320735436113\)	\([2]\)	\(2359296\)	\(2.4487\)
140679.o2	140679i2	\([1, -1, 1, -334949, 69693068]\)	\(48455467135993/3635004681\)	\(311760251306212401\)	\([2, 2]\)	\(1179648\)	\(2.1021\)
140679.o3	140679i1	\([1, -1, 1, -68144, -5545942]\)	\(408023180713/80247321\)	\(6882501442811841\)	\([2]\)	\(589824\)	\(1.7556\)	\(\Gamma_0(N)\)-optimal
140679.o4	140679i4	\([1, -1, 1, 319936, 308595116]\)	\(42227808999767/504359959257\)	\(-43256997293190932097\)	\([2]\)	\(2359296\)	\(2.4487\)

Rank

The elliptic curves in class 140679.o have rank \(1\).

Complex multiplication

The elliptic curves in class 140679.o do not have complex multiplication.

Modular form 140679.2.a.o

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.