Elliptic curve isogeny class with LMFDB label 6630.v (Cremona label 6630w)

• Label: 6630.v
• Number of curves: $8$
• Conductor: $6630$
• CM: no
• Rank: $1$

Elliptic curves in class 6630.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6630.v1	6630w7	\([1, 0, 0, -6591000006, -205956849489264]\)	\(31664865542564944883878115208137569/103216295812500\)	\(103216295812500\)	\([2]\)	\(3317760\)	\(3.7742\)
6630.v2	6630w6	\([1, 0, 0, -411937506, -3218101426764]\)	\(7730680381889320597382223137569/441370202660156250000\)	\(441370202660156250000\)	\([2, 2]\)	\(1658880\)	\(3.4276\)
6630.v3	6630w8	\([1, 0, 0, -411190526, -3230353542120]\)	\(-7688701694683937879808871873249/58423707246780395507812500\)	\(-58423707246780395507812500\)	\([2]\)	\(3317760\)	\(3.7742\)
6630.v4	6630w4	\([1, 0, 0, -81373266, -282504599100]\)	\(59589391972023341137821784609/8834417507562311995200\)	\(8834417507562311995200\)	\([6]\)	\(1105920\)	\(3.2249\)
6630.v5	6630w3	\([1, 0, 0, -25792786, -50092914940]\)	\(1897660325010178513043539489/14258428094958372000000\)	\(14258428094958372000000\)	\([4]\)	\(829440\)	\(3.0811\)
6630.v6	6630w2	\([1, 0, 0, -5557266, -3547208700]\)	\(18980483520595353274840609/5549773448629762560000\)	\(5549773448629762560000\)	\([2, 6]\)	\(552960\)	\(2.8783\)
6630.v7	6630w1	\([1, 0, 0, -2096146, 1124611076]\)	\(1018563973439611524445729/42904970360310988800\)	\(42904970360310988800\)	\([12]\)	\(276480\)	\(2.5317\)	\(\Gamma_0(N)\)-optimal
6630.v8	6630w5	\([1, 0, 0, 14880814, -23572439484]\)	\(364421318680576777174674911/450962301637624725000000\)	\(-450962301637624725000000\)	\([6]\)	\(1105920\)	\(3.2249\)

Rank

The elliptic curves in class 6630.v have rank \(1\).

Complex multiplication

The elliptic curves in class 6630.v do not have complex multiplication.

Modular form 6630.2.a.v

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.