Elliptic curve isogeny class with LMFDB label 435600.fs (Cremona label 435600fs)

• Label: 435600.fs
• Number of curves: $4$
• Conductor: $435600$
• CM: no
• Rank: $0$

Elliptic curves in class 435600.fs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435600.fs1	435600fs4	\([0, 0, 0, -6806150175, 216122709888250]\)	\(6749703004355978704/5671875\)	\(29300179546687500000000\)	\([2]\)	\(159252480\)	\(4.0465\)	\(\Gamma_0(N)\)-optimal^*
435600.fs2	435600fs3	\([0, 0, 0, -425290800, 3378477466375]\)	\(-26348629355659264/24169921875\)	\(-7803669978698730468750000\)	\([2]\)	\(79626240\)	\(3.7000\)	\(\Gamma_0(N)\)-optimal^*
435600.fs3	435600fs2	\([0, 0, 0, -85931175, 282320739250]\)	\(13584145739344/1195803675\)	\(6177368573899944300000000\)	\([2]\)	\(53084160\)	\(3.4972\)	\(\Gamma_0(N)\)-optimal^*
435600.fs4	435600fs1	\([0, 0, 0, 5953200, 20542154875]\)	\(72268906496/606436875\)	\(-195798449820739218750000\)	\([2]\)	\(26542080\)	\(3.1506\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 435600.fs1.

Rank

The elliptic curves in class 435600.fs have rank \(0\).

Complex multiplication

The elliptic curves in class 435600.fs do not have complex multiplication.

Modular form 435600.2.a.fs

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 LMFDB 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 LMFDB labels.