Elliptic curve isogeny class with LMFDB label 10710.n (Cremona label 10710l)

• Label: 10710.n
• Number of curves: $8$
• Conductor: $10710$
• CM: no
• Rank: $1$

Elliptic curves in class 10710.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
10710.n1	10710l8	\([1, -1, 0, -119698794, 503716997808]\)	\(260174968233082037895439009/223081361502731896500\)	\(162626312535491552548500\)	\([6]\)	\(1769472\)	\(3.3805\)
10710.n2	10710l7	\([1, -1, 0, -78613794, -265421985192]\)	\(73704237235978088924479009/899277423164136103500\)	\(655573241486655219451500\)	\([6]\)	\(1769472\)	\(3.3805\)
10710.n3	10710l4	\([1, -1, 0, -78382134, -267080313420]\)	\(73054578035931991395831649/136386452160\)	\(99425723624640\)	\([2]\)	\(589824\)	\(2.8312\)
10710.n4	10710l6	\([1, -1, 0, -9156294, 4087006308]\)	\(116454264690812369959009/57505157319440250000\)	\(41921259685871942250000\)	\([2, 6]\)	\(884736\)	\(3.0340\)
10710.n5	10710l5	\([1, -1, 0, -5143734, -3731921100]\)	\(20645800966247918737249/3688936444974392640\)	\(2689234668386332234560\)	\([2]\)	\(589824\)	\(2.8312\)
10710.n6	10710l2	\([1, -1, 0, -4898934, -4172120460]\)	\(17836145204788591940449/770635366502400\)	\(561793182180249600\)	\([2, 2]\)	\(294912\)	\(2.4846\)
10710.n7	10710l1	\([1, -1, 0, -290934, -71922060]\)	\(-3735772816268612449/909650165760000\)	\(-663134970839040000\)	\([2]\)	\(147456\)	\(2.1381\)	\(\Gamma_0(N)\)-optimal
10710.n8	10710l3	\([1, -1, 0, 2093706, 489256308]\)	\(1392333139184610040991/947901937500000000\)	\(-691020512437500000000\)	\([6]\)	\(442368\)	\(2.6874\)

Rank

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

Complex multiplication

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

Modular form 10710.2.a.n

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 12 & 2 & 3 & 6 & 12 & 4 \\ 4 & 1 & 3 & 2 & 12 & 6 & 12 & 4 \\ 12 & 3 & 1 & 6 & 4 & 2 & 4 & 12 \\ 2 & 2 & 6 & 1 & 6 & 3 & 6 & 2 \\ 3 & 12 & 4 & 6 & 1 & 2 & 4 & 12 \\ 6 & 6 & 2 & 3 & 2 & 1 & 2 & 6 \\ 12 & 12 & 4 & 6 & 4 & 2 & 1 & 3 \\ 4 & 4 & 12 & 2 & 12 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.