Elliptic curve isogeny class with Cremona label 10010s (LMFDB label 10010.n)

• Label: 10010s
• Number of curves: $4$
• Conductor: $10010$
• CM: no
• Rank: $0$

Elliptic curves in class 10010s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10010.n3	10010s1	\([1, 0, 0, -2671, 15801]\)	\(2107441550633329/1108665958400\)	\(1108665958400\)	\([6]\)	\(22464\)	\(1.0028\)	\(\Gamma_0(N)\)-optimal
10010.n4	10010s2	\([1, 0, 0, 10129, 125881]\)	\(114926649504265871/73262465436160\)	\(-73262465436160\)	\([6]\)	\(44928\)	\(1.3494\)
10010.n1	10010s3	\([1, 0, 0, -123311, -16676615]\)	\(207362104287019679089/5934929000000\)	\(5934929000000\)	\([2]\)	\(67392\)	\(1.5521\)
10010.n2	10010s4	\([1, 0, 0, -118311, -18089615]\)	\(-183146792453150159089/35223382235041000\)	\(-35223382235041000\)	\([2]\)	\(134784\)	\(1.8987\)

Rank

The elliptic curves in class 10010s have rank \(0\).

Complex multiplication

The elliptic curves in class 10010s do not have complex multiplication.

Modular form 10010.2.a.s

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.