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

• Label: 435600.si
• Number of curves: $4$
• Conductor: $435600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 435600.si have rank \(1\).

Complex multiplication

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

Modular form 435600.2.a.si

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 435600.si

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
435600.si1	435600si3	\([0, 0, 0, -858141075, 9528359805250]\)	\(3382175663521924/59189241375\)	\(1223056149523552278000000000\)	\([2]\)	\(283115520\)	\(3.9942\)	\(\Gamma_0(N)\)-optimal^*
435600.si2	435600si2	\([0, 0, 0, -109453575, -214310632250]\)	\(28071778927696/12404390625\)	\(64079492668605562500000000\)	\([2, 2]\)	\(141557760\)	\(3.6476\)	\(\Gamma_0(N)\)-optimal^*
435600.si3	435600si1	\([0, 0, 0, -92982450, -344943124625]\)	\(275361373935616/148240125\)	\(47861843289514031250000\)	\([2]\)	\(70778880\)	\(3.3010\)	\(\Gamma_0(N)\)-optimal^*
435600.si4	435600si4	\([0, 0, 0, 375695925, -1596501557750]\)	\(283811208976796/217529296875\)	\(-4494913907730468750000000000\)	\([2]\)	\(283115520\)	\(3.9942\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 435600.si1.