Elliptic curve isogeny class with Cremona label 33600gh (LMFDB label 33600.dy)

• Label: 33600gh
• Number of curves: $4$
• Conductor: $33600$
• CM: no
• Rank: $1$

Elliptic curves in class 33600gh

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
33600.dy3	33600gh1	[0, 1, 0, -5633, 100863]	[2]	73728	\(\Gamma_0(N)\)-optimal
33600.dy2	33600gh2	[0, 1, 0, -37633, -2747137]	[2, 2]	147456
33600.dy4	33600gh3	[0, 1, 0, 10367, -9227137]	[2]	294912
33600.dy1	33600gh4	[0, 1, 0, -597633, -178027137]	[2]	294912

Rank

The elliptic curves in class 33600gh have rank \(1\).

Complex multiplication

The elliptic curves in class 33600gh do not have complex multiplication.

Modular form 33600.2.a.gh

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.