Elliptic curve isogeny class with Cremona label 4032z (LMFDB label 4032.r)

• Label: 4032z
• Number of curves: 6
• Conductor: 4032
• CM: no
• Rank: 1

Elliptic curves in class 4032z

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
4032.r5	4032z1	[0, 0, 0, -300, 4048]	[2]	1536	\(\Gamma_0(N)\)-optimal
4032.r4	4032z2	[0, 0, 0, -6060, 181456]	[2]	3072
4032.r6	4032z3	[0, 0, 0, 2580, -84656]	[2]	4608
4032.r3	4032z4	[0, 0, 0, -20460, -923312]	[2]	9216
4032.r2	4032z5	[0, 0, 0, -98220, -11882288]	[2]	13824
4032.r1	4032z6	[0, 0, 0, -1572780, -759189296]	[2]	27648

Rank

The elliptic curves in class 4032z have rank \(1\).

Modular form 4032.2.a.r

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.