Elliptic curve isogeny class with LMFDB label 19890.n (Cremona label 19890r)

• Label: 19890.n
• Number of curves: $8$
• Conductor: $19890$
• CM: no
• Rank: $0$

Elliptic curves in class 19890.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
19890.n1	19890r7	\([1, -1, 0, -59319000054, 5560834936210128]\)	\(31664865542564944883878115208137569/103216295812500\)	\(75244679647312500\)	\([6]\)	\(26542080\)	\(4.3235\)
19890.n2	19890r6	\([1, -1, 0, -3707437554, 86888738522628]\)	\(7730680381889320597382223137569/441370202660156250000\)	\(321758877739253906250000\)	\([2, 6]\)	\(13271040\)	\(3.9769\)
19890.n3	19890r8	\([1, -1, 0, -3700714734, 87219545637240]\)	\(-7688701694683937879808871873249/58423707246780395507812500\)	\(-42590882582902908325195312500\)	\([6]\)	\(26542080\)	\(4.3235\)
19890.n4	19890r4	\([1, -1, 0, -732359394, 7627624175700]\)	\(59589391972023341137821784609/8834417507562311995200\)	\(6440290363012925444500800\)	\([2]\)	\(8847360\)	\(3.7742\)
19890.n5	19890r3	\([1, -1, 0, -232135074, 1352508703380]\)	\(1897660325010178513043539489/14258428094958372000000\)	\(10394394081224653188000000\)	\([6]\)	\(6635520\)	\(3.6304\)
19890.n6	19890r2	\([1, -1, 0, -50015394, 95774634900]\)	\(18980483520595353274840609/5549773448629762560000\)	\(4045784844051096906240000\)	\([2, 2]\)	\(4423680\)	\(3.4276\)
19890.n7	19890r1	\([1, -1, 0, -18865314, -30364499052]\)	\(1018563973439611524445729/42904970360310988800\)	\(31277723392666710835200\)	\([2]\)	\(2211840\)	\(3.0811\)	\(\Gamma_0(N)\)-optimal
19890.n8	19890r5	\([1, -1, 0, 133927326, 636455866068]\)	\(364421318680576777174674911/450962301637624725000000\)	\(-328751517893828424525000000\)	\([2]\)	\(8847360\)	\(3.7742\)

Rank

The elliptic curves in class 19890.n have rank \(0\).

Complex multiplication

The elliptic curves in class 19890.n do not have complex multiplication.

Modular form 19890.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.