Elliptic curve isogeny class with LMFDB label 6006.c (Cremona label 6006i)

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

Elliptic curves in class 6006.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6006.c1	6006i3	\([1, 1, 0, -241131, 44985501]\)	\(1550549616695674282297/19163006232001632\)	\(19163006232001632\)	\([2]\)	\(61440\)	\(1.9343\)
6006.c2	6006i2	\([1, 1, 0, -28171, -715715]\)	\(2472604133104833337/1216813084591104\)	\(1216813084591104\)	\([2, 2]\)	\(30720\)	\(1.5878\)
6006.c3	6006i1	\([1, 1, 0, -23051, -1355715]\)	\(1354635530322645817/1143041163264\)	\(1143041163264\)	\([2]\)	\(15360\)	\(1.2412\)	\(\Gamma_0(N)\)-optimal
6006.c4	6006i4	\([1, 1, 0, 102869, -5354531]\)	\(120384526693766101703/82251930897103968\)	\(-82251930897103968\)	\([2]\)	\(61440\)	\(1.9343\)

Rank

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

Complex multiplication

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

Modular form 6006.2.a.c

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.