Elliptic curve isogeny class with LMFDB label 86394.bt (Cremona label 86394cj)

• Label: 86394.bt
• Number of curves: $4$
• Conductor: $86394$
• CM: no
• Rank: $1$

Elliptic curves in class 86394.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86394.bt1	86394cj4	\([1, 1, 1, -8294129, -9197451493]\)	\(35618855581745079337/188166132\)	\(333347780972052\)	\([2]\)	\(2211840\)	\(2.4032\)
86394.bt2	86394cj2	\([1, 1, 1, -518669, -143705869]\)	\(8710408612492777/19986042384\)	\(35406493231841424\)	\([2, 2]\)	\(1105920\)	\(2.0566\)
86394.bt3	86394cj3	\([1, 1, 1, -332329, -248130805]\)	\(-2291249615386537/13671036998388\)	\(-24219075975901243668\)	\([2]\)	\(2211840\)	\(2.4032\)
86394.bt4	86394cj1	\([1, 1, 1, -44349, -461229]\)	\(5445273626857/3103398144\)	\(5497859119382784\)	\([4]\)	\(552960\)	\(1.7101\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 86394.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 86394.bt do not have complex multiplication.

Modular form 86394.2.a.bt

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.