Elliptic curve isogeny class with Cremona label 490245bt (LMFDB label 490245.bt)

• Label: 490245bt
• Number of curves: $4$
• Conductor: $490245$
• CM: no
• Rank: $0$

Elliptic curves in class 490245bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490245.bt4	490245bt1	\([1, 0, 1, 2081, -67819]\)	\(8477185319/21880935\)	\(-2574270121815\)	\([2]\)	\(737280\)	\(1.0651\)	\(\Gamma_0(N)\)-optimal^*
490245.bt3	490245bt2	\([1, 0, 1, -17764, -766363]\)	\(5268932332201/900900225\)	\(105990010571025\)	\([2, 2]\)	\(1474560\)	\(1.4117\)	\(\Gamma_0(N)\)-optimal^*
490245.bt2	490245bt3	\([1, 0, 1, -81709, 8262671]\)	\(512787603508921/45649063125\)	\(5370566627593125\)	\([2]\)	\(2949120\)	\(1.7583\)	\(\Gamma_0(N)\)-optimal^*
490245.bt1	490245bt4	\([1, 0, 1, -271339, -54422833]\)	\(18778886261717401/732035835\)	\(86123283951915\)	\([2]\)	\(2949120\)	\(1.7583\)

^*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 490245bt1.

Rank

The elliptic curves in class 490245bt have rank \(0\).

Complex multiplication

The elliptic curves in class 490245bt do not have complex multiplication.

Modular form 490245.2.a.bt

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.