Elliptic curve isogeny class with LMFDB label 288.b (Cremona label 288b)

• Label: 288.b
• Number of curves: $4$
• Conductor: $288$
• CM: no
• Rank: $1$

Elliptic curves in class 288.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
288.b1	288b2	\([0, 0, 0, -291, -1910]\)	\(7301384/3\)	\(1119744\)	\([2]\)	\(64\)	\(0.12309\)
288.b2	288b3	\([0, 0, 0, -156, 736]\)	\(140608/3\)	\(8957952\)	\([4]\)	\(64\)	\(0.12309\)
288.b3	288b1	\([0, 0, 0, -21, -20]\)	\(21952/9\)	\(419904\)	\([2, 2]\)	\(32\)	\(-0.22349\)	\(\Gamma_0(N)\)-optimal
288.b4	288b4	\([0, 0, 0, 69, -146]\)	\(97336/81\)	\(-30233088\)	\([2]\)	\(64\)	\(0.12309\)

Rank

The elliptic curves in class 288.b have rank \(1\).

Complex multiplication

The elliptic curves in class 288.b do not have complex multiplication.

Modular form 288.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.