Elliptic curve isogeny class with LMFDB label 257600.dt (Cremona label 257600dt)

• Label: 257600.dt
• Number of curves: $4$
• Conductor: $257600$
• CM: no
• Rank: $1$

Elliptic curves in class 257600.dt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
257600.dt1	257600dt4	\([0, 0, 0, -13738700, -19600474000]\)	\(70016546394529281/1610\)	\(6594560000000\)	\([2]\)	\(4718592\)	\(2.4343\)
257600.dt2	257600dt2	\([0, 0, 0, -858700, -306234000]\)	\(17095749786081/2592100\)	\(10617241600000000\)	\([2, 2]\)	\(2359296\)	\(2.0878\)
257600.dt3	257600dt3	\([0, 0, 0, -778700, -365594000]\)	\(-12748946194881/6718982410\)	\(-27520951951360000000\)	\([4]\)	\(4718592\)	\(2.4343\)
257600.dt4	257600dt1	\([0, 0, 0, -58700, -3834000]\)	\(5461074081/1610000\)	\(6594560000000000\)	\([2]\)	\(1179648\)	\(1.7412\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 257600.dt have rank \(1\).

Complex multiplication

The elliptic curves in class 257600.dt do not have complex multiplication.

Modular form 257600.2.a.dt

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.