Elliptic curve isogeny class with LMFDB label 273273.t (Cremona label 273273t)

• Label: 273273.t
• Number of curves: $4$
• Conductor: $273273$
• CM: no
• Rank: $1$

Elliptic curves in class 273273.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
273273.t1	273273t4	\([1, 0, 0, -30635732, -65268881133]\)	\(5599640476399033/19792773\)	\(11239707199327299693\)	\([2]\)	\(14450688\)	\(2.8741\)
273273.t2	273273t3	\([1, 0, 0, -5709922, 4010610785]\)	\(36254831403673/8741423691\)	\(4963985733181647503331\)	\([2]\)	\(14450688\)	\(2.8741\)
273273.t3	273273t2	\([1, 0, 0, -1942067, -989332800]\)	\(1426487591593/81162081\)	\(46089450231561057321\)	\([2, 2]\)	\(7225344\)	\(2.5275\)
273273.t4	273273t1	\([1, 0, 0, 86778, -62962173]\)	\(127263527/3090087\)	\(-1754765393431617567\)	\([2]\)	\(3612672\)	\(2.1809\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 273273.t have rank \(1\).

Complex multiplication

The elliptic curves in class 273273.t do not have complex multiplication.

Modular form 273273.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.