Elliptic curve isogeny class with Cremona label 171600ey (LMFDB label 171600.du)

• Label: 171600ey
• Number of curves: $4$
• Conductor: $171600$
• CM: no
• Rank: $1$

Elliptic curves in class 171600ey

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
171600.du4	171600ey1	\([0, -1, 0, 8592, 17445312]\)	\(1095912791/2055596400\)	\(-131558169600000000\)	\([2]\)	\(1769472\)	\(1.9638\)	\(\Gamma_0(N)\)-optimal
171600.du3	171600ey2	\([0, -1, 0, -959408, 354309312]\)	\(1525998818291689/37268302500\)	\(2385171360000000000\)	\([2, 2]\)	\(3538944\)	\(2.3104\)
171600.du1	171600ey3	\([0, -1, 0, -15259408, 22948309312]\)	\(6139836723518159689/3799803150\)	\(243187401600000000\)	\([2]\)	\(7077888\)	\(2.6570\)
171600.du2	171600ey4	\([0, -1, 0, -2147408, -695882688]\)	\(17111482619973769/6627044531250\)	\(424130850000000000000\)	\([2]\)	\(7077888\)	\(2.6570\)

Rank

The elliptic curves in class 171600ey have rank \(1\).

Complex multiplication

The elliptic curves in class 171600ey do not have complex multiplication.

Modular form 171600.2.a.ey

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.