Elliptic curve isogeny class with LMFDB label 480240.bp (Cremona label 480240bp)

• Label: 480240.bp
• Number of curves: $4$
• Conductor: $480240$
• CM: no
• Rank: $1$

Elliptic curves in class 480240.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
480240.bp1	480240bp3	\([0, 0, 0, -797403, 274062922]\)	\(18778886261717401/732035835\)	\(2185847290736640\)	\([2]\)	\(3932160\)	\(2.0278\)	\(\Gamma_0(N)\)-optimal^*
480240.bp2	480240bp4	\([0, 0, 0, -240123, -41660822]\)	\(512787603508921/45649063125\)	\(136307372106240000\)	\([2]\)	\(3932160\)	\(2.0278\)
480240.bp3	480240bp2	\([0, 0, 0, -52203, 3853402]\)	\(5268932332201/900900225\)	\(2690073657446400\)	\([2, 2]\)	\(1966080\)	\(1.6812\)	\(\Gamma_0(N)\)-optimal^*
480240.bp4	480240bp1	\([0, 0, 0, 6117, 342538]\)	\(8477185319/21880935\)	\(-65336121815040\)	\([2]\)	\(983040\)	\(1.3346\)	\(\Gamma_0(N)\)-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 480240.bp1.

Rank

The elliptic curves in class 480240.bp have rank \(1\).

Complex multiplication

The elliptic curves in class 480240.bp do not have complex multiplication.

Modular form 480240.2.a.bp

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.