Elliptic curve isogeny class with Cremona label 1008h (LMFDB label 1008.d)

• Label: 1008h
• Number of curves: $4$
• Conductor: $1008$
• CM: no
• Rank: $1$

Elliptic curves in class 1008h

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
1008.d4	1008h1	[0, 0, 0, 9, 54]	[2]	128	\(\Gamma_0(N)\)-optimal
1008.d3	1008h2	[0, 0, 0, -171, 810]	[2, 2]	256
1008.d2	1008h3	[0, 0, 0, -531, -3726]	[2]	512
1008.d1	1008h4	[0, 0, 0, -2691, 53730]	[2]	512

Rank

The elliptic curves in class 1008h have rank \(1\).

Complex multiplication

The elliptic curves in class 1008h do not have complex multiplication.

Modular form 1008.2.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.