Elliptic curve isogeny class with Cremona label 111600fn (LMFDB label 111600.i)

• Label: 111600fn
• Number of curves: $4$
• Conductor: $111600$
• CM: no
• Rank: $2$

Elliptic curves in class 111600fn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
111600.i3	111600fn1	\([0, 0, 0, -36075, -2627750]\)	\(111284641/465\)	\(21695040000000\)	\([2]\)	\(393216\)	\(1.4138\)	\(\Gamma_0(N)\)-optimal
111600.i2	111600fn2	\([0, 0, 0, -54075, 270250]\)	\(374805361/216225\)	\(10088193600000000\)	\([2, 2]\)	\(786432\)	\(1.7604\)
111600.i4	111600fn3	\([0, 0, 0, 215925, 2160250]\)	\(23862997439/13852815\)	\(-646316936640000000\)	\([4]\)	\(1572864\)	\(2.1070\)
111600.i1	111600fn4	\([0, 0, 0, -612075, 183852250]\)	\(543538277281/1569375\)	\(73220760000000000\)	\([2]\)	\(1572864\)	\(2.1070\)

Rank

The elliptic curves in class 111600fn have rank \(2\).

Complex multiplication

The elliptic curves in class 111600fn do not have complex multiplication.

Modular form 111600.2.a.fn

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.