Elliptic curve isogeny class with Cremona label 33600gf (LMFDB label 33600.ey)

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

Elliptic curves in class 33600gf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
33600.ey3	33600gf1	\([0, 1, 0, -1984508, 1075376238]\)	\(864335783029582144/59535\)	\(59535000000\)	\([2]\)	\(368640\)	\(1.9684\)	\(\Gamma_0(N)\)-optimal
33600.ey2	33600gf2	\([0, 1, 0, -1984633, 1075233863]\)	\(13507798771700416/3544416225\)	\(226842638400000000\)	\([2, 2]\)	\(737280\)	\(2.3150\)
33600.ey4	33600gf3	\([0, 1, 0, -1741633, 1348608863]\)	\(-1141100604753992/875529151875\)	\(-448270925760000000000\)	\([2]\)	\(1474560\)	\(2.6615\)
33600.ey1	33600gf4	\([0, 1, 0, -2229633, 792748863]\)	\(2394165105226952/854262178245\)	\(437382235261440000000\)	\([2]\)	\(1474560\)	\(2.6615\)

Rank

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

Complex multiplication

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

Modular form 33600.2.a.gf

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.