Elliptic curve isogeny class with Cremona label 72450bk (LMFDB label 72450.b)

• Label: 72450bk
• Number of curves: $4$
• Conductor: $72450$
• CM: no
• Rank: $1$

Elliptic curves in class 72450bk

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
72450.b4	72450bk1	[1, -1, 0, 1045008, -2896035584]	[2]	5529600	\(\Gamma_0(N)\)-optimal
72450.b2	72450bk2	[1, -1, 0, -25198992, -46382343584]	[2]	11059200
72450.b3	72450bk3	[1, -1, 0, -9434367, 79561974541]	[2]	16588800
72450.b1	72450bk4	[1, -1, 0, -341210367, 2414269686541]	[2]	33177600

Rank

The elliptic curves in class 72450bk have rank \(1\).

Complex multiplication

The elliptic curves in class 72450bk do not have complex multiplication.

Modular form 72450.2.a.bk

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.