Elliptic curve isogeny class with LMFDB label 257754.ba (Cremona label 257754ba)

• Label: 257754.ba
• Number of curves: $4$
• Conductor: $257754$
• CM: no
• Rank: $2$

Elliptic curves in class 257754.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
257754.ba1	257754ba3	\([1, 0, 1, -14455892, 21024564716]\)	\(7101281816103496897/50099889941262\)	\(2356993460289709041822\)	\([2]\)	\(28753920\)	\(2.9337\)
257754.ba2	257754ba2	\([1, 0, 1, -1492382, -152625220]\)	\(7813429445648737/4308107057604\)	\(202678691967297929124\)	\([2, 2]\)	\(14376960\)	\(2.5871\)
257754.ba3	257754ba1	\([1, 0, 1, -1138602, -467064884]\)	\(3469903405095457/5695440912\)	\(267947035388483472\)	\([2]\)	\(7188480\)	\(2.2405\)	\(\Gamma_0(N)\)-optimal
257754.ba4	257754ba4	\([1, 0, 1, 5810648, -1204261540]\)	\(461185788415532543/280217554681806\)	\(-13183081731671237941086\)	\([2]\)	\(28753920\)	\(2.9337\)

Rank

The elliptic curves in class 257754.ba have rank \(2\).

Complex multiplication

The elliptic curves in class 257754.ba do not have complex multiplication.

Modular form 257754.2.a.ba

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.