Elliptic curve isogeny class with Cremona label 210210cc (LMFDB label 210210.di)

• Label: 210210cc
• Number of curves: $4$
• Conductor: $210210$
• CM: no
• Rank: $2$

Elliptic curves in class 210210cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
210210.di4	210210cc1	\([1, 1, 1, 53605, 10336745]\)	\(144794100308831/474439680000\)	\(-55817353912320000\)	\([2]\)	\(2359296\)	\(1.8965\)	\(\Gamma_0(N)\)-optimal
210210.di3	210210cc2	\([1, 1, 1, -510875, 121200617]\)	\(125337052492018849/18404100000000\)	\(2165223960900000000\)	\([2, 2]\)	\(4718592\)	\(2.2431\)
210210.di1	210210cc3	\([1, 1, 1, -7860875, 8479620617]\)	\(456612868287073618849/12544848030000\)	\(1475888825881470000\)	\([2]\)	\(9437184\)	\(2.5897\)
210210.di2	210210cc4	\([1, 1, 1, -2192555, -1130641975]\)	\(9908022260084596129/1047363281250000\)	\(123221242675781250000\)	\([2]\)	\(9437184\)	\(2.5897\)

Rank

The elliptic curves in class 210210cc have rank \(2\).

Complex multiplication

The elliptic curves in class 210210cc do not have complex multiplication.

Modular form 210210.2.a.cc

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.