Elliptic curve isogeny class with LMFDB label 44770.b (Cremona label 44770j)

• Label: 44770.b
• Number of curves: $4$
• Conductor: $44770$
• CM: no
• Rank: $2$

Elliptic curves in class 44770.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44770.b1	44770j3	\([1, 0, 1, -638278, 196220616]\)	\(16232905099479601/4052240\)	\(7178790346640\)	\([2]\)	\(414720\)	\(1.8425\)
44770.b2	44770j4	\([1, 0, 1, -635858, 197782968]\)	\(-16048965315233521/256572640900\)	\(-454534084285444900\)	\([2]\)	\(829440\)	\(2.1890\)
44770.b3	44770j1	\([1, 0, 1, -9078, 181256]\)	\(46694890801/18944000\)	\(33560451584000\)	\([2]\)	\(138240\)	\(1.2931\)	\(\Gamma_0(N)\)-optimal
44770.b4	44770j2	\([1, 0, 1, 29642, 1327368]\)	\(1625964918479/1369000000\)	\(-2425267009000000\)	\([2]\)	\(276480\)	\(1.6397\)

Rank

The elliptic curves in class 44770.b have rank \(2\).

Complex multiplication

The elliptic curves in class 44770.b do not have complex multiplication.

Modular form 44770.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.