Elliptic curve isogeny class with Cremona label 10710j (LMFDB label 10710.i)

• Label: 10710j
• Number of curves: $4$
• Conductor: $10710$
• CM: no
• Rank: $1$

Elliptic curves in class 10710j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10710.i4	10710j1	\([1, -1, 0, -39669, -5660875]\)	\(-9470133471933009/13576123187200\)	\(-9896993803468800\)	\([2]\)	\(86016\)	\(1.7614\)	\(\Gamma_0(N)\)-optimal
10710.i3	10710j2	\([1, -1, 0, -776949, -263266507]\)	\(71149857462630609489/41907496960000\)	\(30550565283840000\)	\([2, 2]\)	\(172032\)	\(2.1079\)
10710.i1	10710j3	\([1, -1, 0, -12429429, -16863389515]\)	\(291306206119284545407569/101150000000\)	\(73738350000000\)	\([2]\)	\(344064\)	\(2.4545\)
10710.i2	10710j4	\([1, -1, 0, -920949, -158751307]\)	\(118495863754334673489/53596139570691200\)	\(39071585747033884800\)	\([2]\)	\(344064\)	\(2.4545\)

Rank

The elliptic curves in class 10710j have rank \(1\).

Complex multiplication

The elliptic curves in class 10710j do not have complex multiplication.

Modular form 10710.2.a.j

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.