Elliptic curve isogeny class with LMFDB label 28224.ft (Cremona label 28224dz)

• Label: 28224.ft
• Number of curves: $2$
• Conductor: $28224$
• CM: no
• Rank: $1$

Elliptic curves in class 28224.ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28224.ft1	28224dz2	\([0, 0, 0, -53676, -4786992]\)	\(-67645179/8\)	\(-2022633897984\)	\([]\)	\(82944\)	\(1.3868\)
28224.ft2	28224dz1	\([0, 0, 0, 84, -20272]\)	\(189/512\)	\(-177570054144\)	\([]\)	\(27648\)	\(0.83750\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 28224.ft have rank \(1\).

Complex multiplication

The elliptic curves in class 28224.ft do not have complex multiplication.

Modular form 28224.2.a.ft

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.