Elliptic curve isogeny class with LMFDB label 444675.fx (Cremona label 444675fx)

• Label: 444675.fx
• Number of curves: $4$
• Conductor: $444675$
• CM: no
• Rank: $1$

Elliptic curves in class 444675.fx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
444675.fx1	444675fx3	\([1, 1, 0, -3068631150, -18538402849875]\)	\(981281029968144361/522287841796875\)	\(1700882423107059093475341796875\)	\([2]\)	\(637009920\)	\(4.4921\)	\(\Gamma_0(N)\)-optimal^*
444675.fx2	444675fx2	\([1, 1, 0, -2408288775, -45440090865000]\)	\(474334834335054841/607815140625\)	\(1979410597862386484619140625\)	\([2, 2]\)	\(318504960\)	\(4.1455\)	\(\Gamma_0(N)\)-optimal^*
444675.fx3	444675fx1	\([1, 1, 0, -2407547650, -45469484623625]\)	\(473897054735271721/779625\)	\(2538926532451353515625\)	\([2]\)	\(159252480\)	\(3.7990\)	\(\Gamma_0(N)\)-optimal^*
444675.fx4	444675fx4	\([1, 1, 0, -1759804400, -70460563505625]\)	\(-185077034913624841/551466161890875\)	\(-1795904531247530565481060546875\)	\([2]\)	\(637009920\)	\(4.4921\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 444675.fx1.

Rank

The elliptic curves in class 444675.fx have rank \(1\).

Complex multiplication

The elliptic curves in class 444675.fx do not have complex multiplication.

Modular form 444675.2.a.fx

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.