Elliptic curve isogeny class with LMFDB label 8050.g (Cremona label 8050l)

• Label: 8050.g
• Number of curves: $4$
• Conductor: $8050$
• CM: no
• Rank: $1$

Elliptic curves in class 8050.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8050.g1	8050l3	\([1, -1, 0, -214667, -38228509]\)	\(70016546394529281/1610\)	\(25156250\)	\([2]\)	\(24576\)	\(1.3946\)
8050.g2	8050l2	\([1, -1, 0, -13417, -594759]\)	\(17095749786081/2592100\)	\(40501562500\)	\([2, 2]\)	\(12288\)	\(1.0480\)
8050.g3	8050l4	\([1, -1, 0, -12167, -711009]\)	\(-12748946194881/6718982410\)	\(-104984100156250\)	\([2]\)	\(24576\)	\(1.3946\)
8050.g4	8050l1	\([1, -1, 0, -917, -7259]\)	\(5461074081/1610000\)	\(25156250000\)	\([2]\)	\(6144\)	\(0.70147\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 8050.g have rank \(1\).

Complex multiplication

The elliptic curves in class 8050.g do not have complex multiplication.

Modular form 8050.2.a.g

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.