Elliptic curve isogeny class with Cremona label 466440cg (LMFDB label 466440.cg)

• Label: 466440cg
• Number of curves: $4$
• Conductor: $466440$
• CM: no
• Rank: $1$

Elliptic curves in class 466440cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
466440.cg4	466440cg1	\([0, 1, 0, -668620, -1347162400]\)	\(-26752376766544/618796614375\)	\(-764624145263303520000\)	\([2]\)	\(14155776\)	\(2.6879\)	\(\Gamma_0(N)\)-optimal^*
466440.cg3	466440cg2	\([0, 1, 0, -22844800, -41849737552]\)	\(266763091319403556/1355769140625\)	\(6701095618448400000000\)	\([2, 2]\)	\(28311552\)	\(3.0345\)	\(\Gamma_0(N)\)-optimal^*
466440.cg2	466440cg3	\([0, 1, 0, -35438680, 9412391600]\)	\(497927680189263938/284271240234375\)	\(2810107864687500000000000\)	\([2]\)	\(56623104\)	\(3.3810\)	\(\Gamma_0(N)\)-optimal^*
466440.cg1	466440cg4	\([0, 1, 0, -365069800, -2684921857552]\)	\(544328872410114151778/14166950625\)	\(140044625468017920000\)	\([2]\)	\(56623104\)	\(3.3810\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 466440cg1.

Rank

The elliptic curves in class 466440cg have rank \(1\).

Complex multiplication

The elliptic curves in class 466440cg do not have complex multiplication.

Modular form 466440.2.a.cg

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.