Elliptic curve isogeny class with Cremona label 444360b (LMFDB label 444360.b)

• Label: 444360b
• Number of curves: $4$
• Conductor: $444360$
• CM: no
• Rank: $0$

Elliptic curves in class 444360b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
444360.b3	444360b1	\([0, -1, 0, -600591, -178917420]\)	\(10115186538496/2113125\)	\(5005093407090000\)	\([2]\)	\(7028736\)	\(2.0087\)	\(\Gamma_0(N)\)-optimal^*
444360.b2	444360b2	\([0, -1, 0, -666716, -137020620]\)	\(864848456656/285779025\)	\(10830221317997625600\)	\([2, 2]\)	\(14057472\)	\(2.3553\)	\(\Gamma_0(N)\)-optimal^*
444360.b1	444360b3	\([0, -1, 0, -4316816, 3351014940]\)	\(58687749106564/1988856345\)	\(301488247936374481920\)	\([2]\)	\(28114944\)	\(2.7018\)	\(\Gamma_0(N)\)-optimal^*
444360.b4	444360b4	\([0, -1, 0, 1925384, -944718980]\)	\(5207251926236/5553444645\)	\(-841839733795701150720\)	\([2]\)	\(28114944\)	\(2.7018\)

^*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 444360b1.

Rank

The elliptic curves in class 444360b have rank \(0\).

Complex multiplication

The elliptic curves in class 444360b do not have complex multiplication.

Modular form 444360.2.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 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.