Elliptic curve isogeny class with Cremona label 16650r (LMFDB label 16650.w)

• Label: 16650r
• Number of curves: $4$
• Conductor: $16650$
• CM: no
• Rank: $1$

Elliptic curves in class 16650r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16650.w3	16650r1	\([1, -1, 0, -1167, -12259]\)	\(15438249/2960\)	\(33716250000\)	\([2]\)	\(12288\)	\(0.73739\)	\(\Gamma_0(N)\)-optimal
16650.w2	16650r2	\([1, -1, 0, -5667, 154241]\)	\(1767172329/136900\)	\(1559376562500\)	\([2, 2]\)	\(24576\)	\(1.0840\)
16650.w1	16650r3	\([1, -1, 0, -88917, 10227491]\)	\(6825481747209/46250\)	\(526816406250\)	\([2]\)	\(49152\)	\(1.4305\)
16650.w4	16650r4	\([1, -1, 0, 5583, 682991]\)	\(1689410871/18741610\)	\(-213478651406250\)	\([2]\)	\(49152\)	\(1.4305\)

Rank

The elliptic curves in class 16650r have rank \(1\).

Complex multiplication

The elliptic curves in class 16650r do not have complex multiplication.

Modular form 16650.2.a.r

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.