Elliptic curve isogeny class with LMFDB label 6600.r (Cremona label 6600q)

• Label: 6600.r
• Number of curves: $4$
• Conductor: $6600$
• CM: no
• Rank: $1$

Elliptic curves in class 6600.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6600.r1	6600q3	\([0, 1, 0, -264008, -52300512]\)	\(127191074376964/495\)	\(7920000000\)	\([2]\)	\(24576\)	\(1.5355\)
6600.r2	6600q2	\([0, 1, 0, -16508, -820512]\)	\(124386546256/245025\)	\(980100000000\)	\([2, 2]\)	\(12288\)	\(1.1890\)
6600.r3	6600q4	\([0, 1, 0, -11008, -1370512]\)	\(-9220796644/45106875\)	\(-721710000000000\)	\([2]\)	\(24576\)	\(1.5355\)
6600.r4	6600q1	\([0, 1, 0, -1383, -3762]\)	\(1171019776/658845\)	\(164711250000\)	\([4]\)	\(6144\)	\(0.84239\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 6600.r have rank \(1\).

Complex multiplication

The elliptic curves in class 6600.r do not have complex multiplication.

Modular form 6600.2.a.r

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.