Elliptic curve isogeny class with Cremona label 6006g (LMFDB label 6006.h)

• Label: 6006g
• Number of curves: $4$
• Conductor: $6006$
• CM: no
• Rank: $1$

Elliptic curves in class 6006g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6006.h3	6006g1	\([1, 1, 0, -55764, 5045328]\)	\(19177749277229260873/10959556608\)	\(10959556608\)	\([2]\)	\(15360\)	\(1.2521\)	\(\Gamma_0(N)\)-optimal
6006.h2	6006g2	\([1, 1, 0, -56084, 4984080]\)	\(19509797127983109193/458190464187456\)	\(458190464187456\)	\([2, 2]\)	\(30720\)	\(1.5987\)
6006.h1	6006g3	\([1, 1, 0, -124124, -9562872]\)	\(211493228575739333833/83312312835279528\)	\(83312312835279528\)	\([2]\)	\(61440\)	\(1.9453\)
6006.h4	6006g4	\([1, 1, 0, 6836, 15617560]\)	\(35320805896348727/105350345460143784\)	\(-105350345460143784\)	\([2]\)	\(61440\)	\(1.9453\)

Rank

The elliptic curves in class 6006g have rank \(1\).

Complex multiplication

The elliptic curves in class 6006g do not have complex multiplication.

Modular form 6006.2.a.g

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.