Elliptic curve isogeny class with Cremona label 1734b (LMFDB label 1734.b)

• Label: 1734b
• Number of curves: $4$
• Conductor: $1734$
• CM: no
• Rank: $1$

Elliptic curves in class 1734b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1734.b2	1734b1	\([1, 1, 0, -73845, 7690221]\)	\(1845026709625/793152\)	\(19144761127488\)	\([2]\)	\(6912\)	\(1.5087\)	\(\Gamma_0(N)\)-optimal
1734.b3	1734b2	\([1, 1, 0, -62285, 10194117]\)	\(-1107111813625/1228691592\)	\(-29657628081619848\)	\([2]\)	\(13824\)	\(1.8553\)
1734.b1	1734b3	\([1, 1, 0, -216900, -29485872]\)	\(46753267515625/11591221248\)	\(279783902667866112\)	\([2]\)	\(20736\)	\(2.0580\)
1734.b4	1734b4	\([1, 1, 0, 522940, -186183984]\)	\(655215969476375/1001033261568\)	\(-24162509422392648192\)	\([2]\)	\(41472\)	\(2.4046\)

Rank

The elliptic curves in class 1734b have rank \(1\).

Complex multiplication

The elliptic curves in class 1734b do not have complex multiplication.

Modular form 1734.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.