Elliptic curve isogeny class with Cremona label 476850hs (LMFDB label 476850.hs)

• Label: 476850hs
• Number of curves: $4$
• Conductor: $476850$
• CM: no
• Rank: $0$

Elliptic curves in class 476850hs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
476850.hs3	476850hs1	\([1, 1, 1, -59819538, -160258287969]\)	\(62768149033310713/6915442583808\)	\(2608155820815685668000000\)	\([2]\)	\(141557760\)	\(3.4184\)	\(\Gamma_0(N)\)-optimal^*
476850.hs2	476850hs2	\([1, 1, 1, -226861538, 1143337480031]\)	\(3423676911662954233/483711578981136\)	\(182431587714939373412250000\)	\([2, 2]\)	\(283115520\)	\(3.7650\)	\(\Gamma_0(N)\)-optimal^*
476850.hs1	476850hs3	\([1, 1, 1, -3496463038, 79574538262031]\)	\(12534210458299016895673/315581882565708\)	\(119021554149682404435187500\)	\([2]\)	\(566231040\)	\(4.1116\)	\(\Gamma_0(N)\)-optimal^*
476850.hs4	476850hs4	\([1, 1, 1, 370067962, 6145606690031]\)	\(14861225463775641287/51859390496937804\)	\(-19558744006527820824351187500\)	\([2]\)	\(566231040\)	\(4.1116\)

^*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 476850hs1.

Rank

The elliptic curves in class 476850hs have rank \(0\).

Complex multiplication

The elliptic curves in class 476850hs do not have complex multiplication.

Modular form 476850.2.a.hs

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.