Elliptic curve isogeny class with Cremona label 6084n (LMFDB label 6084.b)

• Label: 6084n
• Number of curves: $2$
• Conductor: $6084$
• CM: no
• Rank: $1$

Elliptic curves in class 6084n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6084.b2	6084n1	\([0, 0, 0, -8112, -252655]\)	\(1048576/117\)	\(6587088320592\)	\([2]\)	\(16128\)	\(1.1927\)	\(\Gamma_0(N)\)-optimal
6084.b1	6084n2	\([0, 0, 0, -30927, 1823510]\)	\(3631696/507\)	\(456704790227712\)	\([2]\)	\(32256\)	\(1.5393\)

Rank

The elliptic curves in class 6084n have rank \(1\).

Complex multiplication

The elliptic curves in class 6084n do not have complex multiplication.

Modular form 6084.2.a.n

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.