Elliptic curve isogeny class with Cremona label 570e (LMFDB label 570.e)

• Label: 570e
• Number of curves: $4$
• Conductor: $570$
• CM: no
• Rank: $1$

Elliptic curves in class 570e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
570.e4	570e1	\([1, 0, 1, 12, -14]\)	\(214921799/218880\)	\(-218880\)	\([2]\)	\(128\)	\(-0.28846\)	\(\Gamma_0(N)\)-optimal
570.e3	570e2	\([1, 0, 1, -68, -142]\)	\(34043726521/11696400\)	\(11696400\)	\([2, 2]\)	\(256\)	\(0.058114\)
570.e1	570e3	\([1, 0, 1, -968, -11662]\)	\(100162392144121/23457780\)	\(23457780\)	\([2]\)	\(512\)	\(0.40469\)
570.e2	570e4	\([1, 0, 1, -448, 3506]\)	\(9912050027641/311647500\)	\(311647500\)	\([4]\)	\(512\)	\(0.40469\)

Rank

The elliptic curves in class 570e have rank \(1\).

Complex multiplication

The elliptic curves in class 570e do not have complex multiplication.

Modular form 570.2.a.e

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.