Elliptic curve isogeny class with LMFDB label 428736.bv (Cremona label 428736bv)

• Label: 428736.bv
• Number of curves: $4$
• Conductor: $428736$
• CM: no
• Rank: $1$

Elliptic curves in class 428736.bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
428736.bv1	428736bv3	\([0, -1, 0, -79969, 8725249]\)	\(215751695207833/163381911\)	\(42829587677184\)	\([2]\)	\(1703936\)	\(1.5483\)	\(\Gamma_0(N)\)-optimal^*
428736.bv2	428736bv2	\([0, -1, 0, -6049, 76609]\)	\(93391282153/44876601\)	\(11764131692544\)	\([2, 2]\)	\(851968\)	\(1.2018\)	\(\Gamma_0(N)\)-optimal^*
428736.bv3	428736bv1	\([0, -1, 0, -3169, -66815]\)	\(13430356633/180873\)	\(47414771712\)	\([2]\)	\(425984\)	\(0.85518\)	\(\Gamma_0(N)\)-optimal^*
428736.bv4	428736bv4	\([0, -1, 0, 21791, 561025]\)	\(4365111505607/3058314567\)	\(-801718813851648\)	\([2]\)	\(1703936\)	\(1.5483\)

^*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 428736.bv1.

Rank

The elliptic curves in class 428736.bv have rank \(1\).

Complex multiplication

The elliptic curves in class 428736.bv do not have complex multiplication.

Modular form 428736.2.a.bv

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.