Elliptic curve isogeny class with Cremona label 34650y (LMFDB label 34650.bl)

• Label: 34650y
• Number of curves: $4$
• Conductor: $34650$
• CM: no
• Rank: $1$

Elliptic curves in class 34650y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
34650.bl4	34650y1	\([1, -1, 0, 57708, -7118384]\)	\(1865864036231/2993760000\)	\(-34100797500000000\)	\([2]\)	\(245760\)	\(1.8575\)	\(\Gamma_0(N)\)-optimal
34650.bl3	34650y2	\([1, -1, 0, -392292, -72368384]\)	\(586145095611769/140040608400\)	\(1595150055056250000\)	\([2, 2]\)	\(491520\)	\(2.2041\)
34650.bl2	34650y3	\([1, -1, 0, -2124792, 1131719116]\)	\(93137706732176569/5369647977540\)	\(61163646494166562500\)	\([2]\)	\(983040\)	\(2.5507\)
34650.bl1	34650y4	\([1, -1, 0, -5859792, -5457855884]\)	\(1953542217204454969/170843779260\)	\(1946017423133437500\)	\([2]\)	\(983040\)	\(2.5507\)

Rank

The elliptic curves in class 34650y have rank \(1\).

Complex multiplication

The elliptic curves in class 34650y do not have complex multiplication.

Modular form 34650.2.a.y

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.