Elliptic curve isogeny class with LMFDB label 474320.dw (Cremona label 474320dw)

• Label: 474320.dw
• Number of curves: $4$
• Conductor: $474320$
• CM: no
• Rank: $0$

Elliptic curves in class 474320.dw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
474320.dw1	474320dw3	\([0, 0, 0, -1983529163, 34002118567802]\)	\(1010962818911303721/57392720\)	\(48996054229735637319680\)	\([2]\)	\(141557760\)	\(3.8204\)	\(\Gamma_0(N)\)-optimal^*
474320.dw2	474320dw4	\([0, 0, 0, -207675083, -271661787782]\)	\(1160306142246441/634128110000\)	\(541353942907040570531840000\)	\([2]\)	\(141557760\)	\(3.8204\)
474320.dw3	474320dw2	\([0, 0, 0, -124194763, 529265098362]\)	\(248158561089321/1859334400\)	\(1587310186616228911513600\)	\([2, 2]\)	\(70778880\)	\(3.4739\)	\(\Gamma_0(N)\)-optimal^*
474320.dw4	474320dw1	\([0, 0, 0, -2768843, 18766245498]\)	\(-2749884201/176619520\)	\(-150779743144250315898880\)	\([2]\)	\(35389440\)	\(3.1273\)	\(\Gamma_0(N)\)-optimal^*

^*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 474320.dw1.

Rank

The elliptic curves in class 474320.dw have rank \(0\).

Complex multiplication

The elliptic curves in class 474320.dw do not have complex multiplication.

Modular form 474320.2.a.dw

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.