Elliptic curve isogeny class with LMFDB label 425880.bq (Cremona label 425880bq)

• Label: 425880.bq
• Number of curves: $4$
• Conductor: $425880$
• CM: no
• Rank: $2$

Elliptic curves in class 425880.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
425880.bq1	425880bq4	\([0, 0, 0, -4405323, -3558511658]\)	\(2624033547076/324135\)	\(1167921161187056640\)	\([2]\)	\(11796480\)	\(2.4901\)
425880.bq2	425880bq2	\([0, 0, 0, -298623, -45640478]\)	\(3269383504/893025\)	\(804435493674758400\)	\([2, 2]\)	\(5898240\)	\(2.1435\)
425880.bq3	425880bq1	\([0, 0, 0, -108498, 13184197]\)	\(2508888064/118125\)	\(6650425708290000\)	\([2]\)	\(2949120\)	\(1.7969\)	\(\Gamma_0(N)\)-optimal^*
425880.bq4	425880bq3	\([0, 0, 0, 766077, -297548498]\)	\(13799183324/18600435\)	\(-67020968558731299840\)	\([2]\)	\(11796480\)	\(2.4901\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 425880.bq1.

Rank

The elliptic curves in class 425880.bq have rank \(2\).

Complex multiplication

The elliptic curves in class 425880.bq do not have complex multiplication.

Modular form 425880.2.a.bq

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.