Elliptic Curve Isogeny Class with LMFDB label 265200.dz (Cremona label 265200dz)

• Label: 265200.dz
• Number of curves: 8
• Conductor: 265200
• CM: no
• Rank: 1

Elliptic curves in class 265200.dz

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
265200.dz1	265200dz7	[0, 1, 0, -2636400002408, 1647649523114107188]	[2]	1911029760
265200.dz2	265200dz6	[0, 1, 0, -164775002408, 25744481864107188]	[2, 2]	955514880
265200.dz3	265200dz8	[0, 1, 0, -164476210408, 25842499384539188]	[2]	1911029760
265200.dz4	265200dz4	[0, 1, 0, -32549306408, 2259971694187188]	[2]	637009920
265200.dz5	265200dz3	[0, 1, 0, -10317114408, 400722685291188]	[2]	477757440
265200.dz6	265200dz2	[0, 1, 0, -2222906408, 28373223787188]	[2, 2]	318504960
265200.dz7	265200dz1	[0, 1, 0, -838458408, -8998565524812]	[2]	159252480	\(\Gamma_0(N)\)-optimal
265200.dz8	265200dz5	[0, 1, 0, 5952325592, 188591420523188]	[2]	637009920

Rank

The elliptic curves in class 265200.dz have rank \(1\).

Modular form 265200.2.a.dz

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.