Elliptic curve isogeny class with Cremona label 333270dm (LMFDB label 333270.dm)

• Label: 333270dm
• Number of curves: $4$
• Conductor: $333270$
• CM: no
• Rank: $1$

Elliptic curves in class 333270dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
333270.dm3	333270dm1	\([1, -1, 1, -16763, -523173]\)	\(4826809/1680\)	\(181302513976080\)	\([2]\)	\(1441792\)	\(1.4375\)	\(\Gamma_0(N)\)-optimal
333270.dm2	333270dm2	\([1, -1, 1, -111983, 14064531]\)	\(1439069689/44100\)	\(4759190991872100\)	\([2, 2]\)	\(2883584\)	\(1.7841\)
333270.dm1	333270dm3	\([1, -1, 1, -1778333, 913226991]\)	\(5763259856089/5670\)	\(611895984669270\)	\([2]\)	\(5767168\)	\(2.1306\)
333270.dm4	333270dm4	\([1, -1, 1, 30847, 47372487]\)	\(30080231/9003750\)	\(-971668160840553750\)	\([2]\)	\(5767168\)	\(2.1306\)

Rank

The elliptic curves in class 333270dm have rank \(1\).

Complex multiplication

The elliptic curves in class 333270dm do not have complex multiplication.

Modular form 333270.2.a.dm

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.