Elliptic curve isogeny class with LMFDB label 163254.t (Cremona label 163254dt)

• Label: 163254.t
• Number of curves: $4$
• Conductor: $163254$
• CM: no
• Rank: $1$

Elliptic curves in class 163254.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163254.t1	163254dt4	\([1, 1, 0, -45275779, -117278089547]\)	\(2126480513962938771457/50232\)	\(242460269688\)	\([2]\)	\(6193152\)	\(2.6334\)
163254.t2	163254dt2	\([1, 1, 0, -2829739, -1833349955]\)	\(519162098474388097/2523253824\)	\(12179264266967616\)	\([2, 2]\)	\(3096576\)	\(2.2868\)
163254.t3	163254dt3	\([1, 1, 0, -2782419, -1897563195]\)	\(-493550314554076417/36254156001336\)	\(-174991886474652616824\)	\([2]\)	\(6193152\)	\(2.6334\)
163254.t4	163254dt1	\([1, 1, 0, -179819, -27694467]\)	\(133221434726017/8821542912\)	\(42579902721527808\)	\([2]\)	\(1548288\)	\(1.9403\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 163254.t have rank \(1\).

Complex multiplication

The elliptic curves in class 163254.t do not have complex multiplication.

Modular form 163254.2.a.t

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.