Elliptic curve isogeny class with Cremona label 281775bj (LMFDB label 281775.bj)

• Label: 281775bj
• Number of curves: $4$
• Conductor: $281775$
• CM: no
• Rank: $1$

Elliptic curves in class 281775bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
281775.bj3	281775bj1	\([1, 1, 0, -188000, 30025875]\)	\(1948441249/89505\)	\(33756767396015625\)	\([2]\)	\(3096576\)	\(1.9331\)	\(\Gamma_0(N)\)-optimal
281775.bj2	281775bj2	\([1, 1, 0, -513125, -102300000]\)	\(39616946929/10989225\)	\(4144580885844140625\)	\([2, 2]\)	\(6193152\)	\(2.2797\)
281775.bj4	281775bj3	\([1, 1, 0, 1329250, -667909125]\)	\(688699320191/910381875\)	\(-343350083190029296875\)	\([2]\)	\(12386304\)	\(2.6263\)
281775.bj1	281775bj4	\([1, 1, 0, -7557500, -7999044375]\)	\(126574061279329/16286595\)	\(6142481415430546875\)	\([2]\)	\(12386304\)	\(2.6263\)

Rank

The elliptic curves in class 281775bj have rank \(1\).

Complex multiplication

The elliptic curves in class 281775bj do not have complex multiplication.

Modular form 281775.2.a.bj

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.