Elliptic curve isogeny class with LMFDB label 123200.dj (Cremona label 123200p)

• Label: 123200.dj
• Number of curves: $4$
• Conductor: $123200$
• CM: no
• Rank: $0$

Elliptic curves in class 123200.dj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
123200.dj1	123200p4	\([0, 0, 0, -33454700, -74478994000]\)	\(1010962818911303721/57392720\)	\(235080581120000000\)	\([2]\)	\(4718592\)	\(2.7998\)
123200.dj2	123200p3	\([0, 0, 0, -3502700, 595054000]\)	\(1160306142246441/634128110000\)	\(2597388738560000000000\)	\([2]\)	\(4718592\)	\(2.7998\)
123200.dj3	123200p2	\([0, 0, 0, -2094700, -1159314000]\)	\(248158561089321/1859334400\)	\(7615833702400000000\)	\([2, 2]\)	\(2359296\)	\(2.4533\)
123200.dj4	123200p1	\([0, 0, 0, -46700, -41106000]\)	\(-2749884201/176619520\)	\(-723433553920000000\)	\([2]\)	\(1179648\)	\(2.1067\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 123200.dj have rank \(0\).

Complex multiplication

The elliptic curves in class 123200.dj do not have complex multiplication.

Modular form 123200.2.a.dj

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.