Elliptic curve isogeny class with Cremona label 73689x (LMFDB label 73689.i)

• Label: 73689x
• Number of curves: $4$
• Conductor: $73689$
• CM: no
• Rank: $1$

Elliptic curves in class 73689x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
73689.i4	73689x1	\([1, 0, 0, 5866, -474957]\)	\(12600539783/62414583\)	\(-110571241074063\)	\([2]\)	\(215040\)	\(1.3770\)	\(\Gamma_0(N)\)-optimal
73689.i3	73689x2	\([1, 0, 0, -67339, -6023896]\)	\(19061979249097/2198953449\)	\(3895580171063889\)	\([2, 2]\)	\(430080\)	\(1.7235\)
73689.i2	73689x3	\([1, 0, 0, -260334, 44733789]\)	\(1101438820807417/148956693039\)	\(263885868076863879\)	\([4]\)	\(860160\)	\(2.0701\)
73689.i1	73689x4	\([1, 0, 0, -1045624, -411620857]\)	\(71366476613135257/1143673377\)	\(2026087151431497\)	\([2]\)	\(860160\)	\(2.0701\)

Rank

The elliptic curves in class 73689x have rank \(1\).

Complex multiplication

The elliptic curves in class 73689x do not have complex multiplication.

Modular form 73689.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.