Elliptic curve isogeny class with Cremona label 444675cs (LMFDB label 444675.cs)

• Label: 444675cs
• Number of curves: $6$
• Conductor: $444675$
• CM: no
• Rank: $0$

Elliptic curves in class 444675cs

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
444675.cs6	444675cs1	[1, 0, 0, 5184787, -1320002849208]	[2]	132710400	\(\Gamma_0(N)\)-optimal^*
444675.cs5	444675cs2	[1, 0, 0, -1774256338, -28255403158333]	[2, 2]	265420800	\(\Gamma_0(N)\)-optimal^*
444675.cs4	444675cs3	[1, 0, 0, -3771588213, 47014048551042]	[2]	530841600	\(\Gamma_0(N)\)-optimal^*
444675.cs2	444675cs4	[1, 0, 0, -28247982463, -1827383356887208]	[2, 2]	530841600
444675.cs3	444675cs5	[1, 0, 0, -28107909838, -1846402838127583]	[2]	1061683200
444675.cs1	444675cs6	[1, 0, 0, -451967673088, -116952447019390333]	[2]	1061683200

^*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 444675cs1.

Rank

The elliptic curves in class 444675cs have rank \(0\).

Complex multiplication

The elliptic curves in class 444675cs do not have complex multiplication.

Modular form 444675.2.a.cs

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.