Elliptic curve isogeny class with Cremona label 221067y (LMFDB label 221067.z)

• Label: 221067y
• Number of curves: $4$
• Conductor: $221067$
• CM: no
• Rank: $0$

Elliptic curves in class 221067y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221067.z3	221067y1	\([1, -1, 0, -168273, -21544880]\)	\(408023180713/80247321\)	\(103636844669561049\)	\([2]\)	\(1474560\)	\(1.9816\)	\(\Gamma_0(N)\)-optimal
221067.z2	221067y2	\([1, -1, 0, -827118, 270323455]\)	\(48455467135993/3635004681\)	\(4694492112676562889\)	\([2, 2]\)	\(2949120\)	\(2.3281\)
221067.z1	221067y3	\([1, -1, 0, -12985803, 18014708344]\)	\(187519537050946633/1186707753\)	\(1532595051563463657\)	\([2]\)	\(5898240\)	\(2.6747\)
221067.z4	221067y4	\([1, -1, 0, 790047, 1197605866]\)	\(42227808999767/504359959257\)	\(-651364732226560539033\)	\([2]\)	\(5898240\)	\(2.6747\)

Rank

The elliptic curves in class 221067y have rank \(0\).

Complex multiplication

The elliptic curves in class 221067y do not have complex multiplication.

Modular form 221067.2.a.y

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.