Elliptic curve isogeny class with Cremona label 211420m (LMFDB label 211420.n)

• Label: 211420m
• Number of curves: $4$
• Conductor: $211420$
• CM: no
• Rank: $1$

Elliptic curves in class 211420m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
211420.n4	211420m1	\([0, -1, 0, -43565, -3413650]\)	\(643956736/15125\)	\(214775890802000\)	\([2]\)	\(1036800\)	\(1.5356\)	\(\Gamma_0(N)\)-optimal
211420.n3	211420m2	\([0, -1, 0, -96420, 6544232]\)	\(436334416/171875\)	\(39050161964000000\)	\([2]\)	\(2073600\)	\(1.8821\)
211420.n2	211420m3	\([0, -1, 0, -427965, 106543970]\)	\(610462990336/8857805\)	\(125781352689283280\)	\([2]\)	\(3110400\)	\(2.0849\)
211420.n1	211420m4	\([0, -1, 0, -6823420, 6862702632]\)	\(154639330142416/33275\)	\(7560111356230400\)	\([2]\)	\(6220800\)	\(2.4314\)

Rank

The elliptic curves in class 211420m have rank \(1\).

Complex multiplication

The elliptic curves in class 211420m do not have complex multiplication.

Modular form 211420.2.a.m

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.