Elliptic curve isogeny class with Cremona label 17160q (LMFDB label 17160.j)

• Label: 17160q
• Number of curves: $4$
• Conductor: $17160$
• CM: no
• Rank: $1$

Elliptic curves in class 17160q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17160.j3	17160q1	\([0, -1, 0, -6436, -196604]\)	\(115185902730064/19305\)	\(4942080\)	\([2]\)	\(16896\)	\(0.68432\)	\(\Gamma_0(N)\)-optimal
17160.j2	17160q2	\([0, -1, 0, -6456, -195300]\)	\(29065753681636/372683025\)	\(381627417600\)	\([2, 2]\)	\(33792\)	\(1.0309\)
17160.j1	17160q3	\([0, -1, 0, -12176, 209676]\)	\(97486245727778/47497539375\)	\(97274960640000\)	\([2]\)	\(67584\)	\(1.3775\)
17160.j4	17160q4	\([0, -1, 0, -1056, -517140]\)	\(-63649751618/56451816135\)	\(-115613319444480\)	\([2]\)	\(67584\)	\(1.3775\)

Rank

The elliptic curves in class 17160q have rank \(1\).

Complex multiplication

The elliptic curves in class 17160q do not have complex multiplication.

Modular form 17160.2.a.q

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.