Elliptic curve isogeny class with LMFDB label 44688.bm (Cremona label 44688m)

• Label: 44688.bm
• Number of curves: $4$
• Conductor: $44688$
• CM: no
• Rank: $1$

Elliptic curves in class 44688.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44688.bm1	44688m4	\([0, -1, 0, -29048392, 60269971168]\)	\(22501000029889239268/3620708343\)	\(436196061025901568\)	\([4]\)	\(2359296\)	\(2.7871\)
44688.bm2	44688m2	\([0, -1, 0, -1821052, 936151840]\)	\(22174957026242512/278654127129\)	\(8392545127065528576\)	\([2, 2]\)	\(1179648\)	\(2.4405\)
44688.bm3	44688m3	\([0, -1, 0, -312832, 2438338960]\)	\(-28104147578308/21301741002339\)	\(-2566275611836601355264\)	\([2]\)	\(2359296\)	\(2.7871\)
44688.bm4	44688m1	\([0, -1, 0, -213607, -14812622]\)	\(572616640141312/280535480757\)	\(528075500409284688\)	\([2]\)	\(589824\)	\(2.0940\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 44688.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 44688.bm do not have complex multiplication.

Modular form 44688.2.a.bm

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.