Elliptic curve isogeny class with Cremona label 650j (LMFDB label 650.l)

• Label: 650j
• Number of curves: $4$
• Conductor: $650$
• CM: no
• Rank: $0$

Elliptic curves in class 650j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
650.l2	650j1	\([1, 1, 1, -813, 8531]\)	\(3803721481/26000\)	\(406250000\)	\([2]\)	\(576\)	\(0.48586\)	\(\Gamma_0(N)\)-optimal
650.l3	650j2	\([1, 1, 1, -313, 19531]\)	\(-217081801/10562500\)	\(-165039062500\)	\([2]\)	\(1152\)	\(0.83244\)
650.l1	650j3	\([1, 1, 1, -5188, -140219]\)	\(988345570681/44994560\)	\(703040000000\)	\([2]\)	\(1728\)	\(1.0352\)
650.l4	650j4	\([1, 1, 1, 2812, -524219]\)	\(157376536199/7722894400\)	\(-120670225000000\)	\([2]\)	\(3456\)	\(1.3817\)

Rank

The elliptic curves in class 650j have rank \(0\).

Complex multiplication

The elliptic curves in class 650j do not have complex multiplication.

Modular form 650.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.