Elliptic curve isogeny class with Cremona label 20216b (LMFDB label 20216.h)

• Label: 20216b
• Number of curves: $4$
• Conductor: $20216$
• CM: no
• Rank: $0$

Elliptic curves in class 20216b

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
20216.h4	20216b1	[0, 0, 0, 361, -13718]	[2]	12096	\(\Gamma_0(N)\)-optimal
20216.h3	20216b2	[0, 0, 0, -6859, -205770]	[2, 2]	24192
20216.h1	20216b3	[0, 0, 0, -107939, -13649410]	[2]	48384
20216.h2	20216b4	[0, 0, 0, -21299, 946542]	[2]	48384

Rank

The elliptic curves in class 20216b have rank \(0\).

Complex multiplication

The elliptic curves in class 20216b do not have complex multiplication.

Modular form 20216.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.