Elliptic curve isogeny class with Cremona label 528h (LMFDB label 528.g)

• Label: 528h
• Number of curves: $4$
• Conductor: $528$
• CM: no
• Rank: $1$

Elliptic curves in class 528h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
528.g3	528h1	\([0, 1, 0, -104, 372]\)	\(30664297/297\)	\(1216512\)	\([2]\)	\(96\)	\(-0.012632\)	\(\Gamma_0(N)\)-optimal
528.g2	528h2	\([0, 1, 0, -184, -364]\)	\(169112377/88209\)	\(361304064\)	\([2, 2]\)	\(192\)	\(0.33394\)
528.g1	528h3	\([0, 1, 0, -2344, -44428]\)	\(347873904937/395307\)	\(1619177472\)	\([2]\)	\(384\)	\(0.68052\)
528.g4	528h4	\([0, 1, 0, 696, -2124]\)	\(9090072503/5845851\)	\(-23944605696\)	\([4]\)	\(384\)	\(0.68052\)

Rank

The elliptic curves in class 528h have rank \(1\).

Complex multiplication

The elliptic curves in class 528h do not have complex multiplication.

Modular form 528.2.a.h

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.