Elliptic curve isogeny class with Cremona label 210e (LMFDB label 210.e)

• Label: 210e
• Number of curves: 8
• Conductor: 210
• CM: no
• Rank: 0

Elliptic curves in class 210e

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
210.e7	210e1	[1, 0, 0, 210, 900]	[8]	128	\(\Gamma_0(N)\)-optimal
210.e6	210e2	[1, 0, 0, -1070, 7812]	[2, 8]	256
210.e5	210e3	[1, 0, 0, -7550, -247500]	[2, 4]	512
210.e4	210e4	[1, 0, 0, -15070, 710612]	[8]	512
210.e2	210e5	[1, 0, 0, -120050, -16020000]	[2, 2]	1024
210.e8	210e6	[1, 0, 0, 1270, -789048]	[4]	1024
210.e1	210e7	[1, 0, 0, -1920800, -1024800150]	[2]	2048
210.e3	210e8	[1, 0, 0, -119300, -16229850]	[2]	2048

Rank

The elliptic curves in class 210e have rank \(0\).

Modular form 210.2.a.e

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.