Elliptic curve isogeny class with Cremona label 308550kd (LMFDB label 308550.kd)

• Label: 308550kd
• Number of curves: $4$
• Conductor: $308550$
• CM: no
• Rank: $1$

Elliptic curves in class 308550kd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
308550.kd3	308550kd1	\([1, 0, 0, -1170738, -487648908]\)	\(6411014266033/296208\)	\(8199227198250000\)	\([2]\)	\(5898240\)	\(2.1288\)	\(\Gamma_0(N)\)-optimal
308550.kd2	308550kd2	\([1, 0, 0, -1231238, -434469408]\)	\(7457162887153/1370924676\)	\(37948073280300562500\)	\([2, 2]\)	\(11796480\)	\(2.4754\)
308550.kd1	308550kd3	\([1, 0, 0, -5859488, 5059263342]\)	\(803760366578833/65593817586\)	\(1815678891819871031250\)	\([2]\)	\(23592960\)	\(2.8219\)
308550.kd4	308550kd4	\([1, 0, 0, 2429012, -2524472158]\)	\(57258048889007/132611470002\)	\(-3670770443878330031250\)	\([2]\)	\(23592960\)	\(2.8219\)

Rank

The elliptic curves in class 308550kd have rank \(1\).

Complex multiplication

The elliptic curves in class 308550kd do not have complex multiplication.

Modular form 308550.2.a.kd

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.