Elliptic curve isogeny class with LMFDB label 2233.b (Cremona label 2233b)

• Label: 2233.b
• Number of curves: $2$
• Conductor: $2233$
• CM: no
• Rank: $1$

Elliptic curves in class 2233.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2233.b1	2233b1	\([0, 1, 1, -63, 271]\)	\(-28094464000/20657483\)	\(-20657483\)	\([3]\)	\(336\)	\(0.10307\)	\(\Gamma_0(N)\)-optimal
2233.b2	2233b2	\([0, 1, 1, 517, -4340]\)	\(15252992000000/17621717267\)	\(-17621717267\)	\([]\)	\(1008\)	\(0.65238\)

Rank

The elliptic curves in class 2233.b have rank \(1\).

Complex multiplication

The elliptic curves in class 2233.b do not have complex multiplication.

Modular form 2233.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.