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 \(1\).

Modular form 1008.2.a.d

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.