Elliptic curve isogeny class with Cremona label 169065bh (LMFDB label 169065.bc)

• Label: 169065bh
• Number of curves: $4$
• Conductor: $169065$
• CM: no
• Rank: $1$

Elliptic curves in class 169065bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
169065.bc3	169065bh1	\([1, -1, 0, -67680, -6485589]\)	\(1948441249/89505\)	\(1574955739628505\)	\([2]\)	\(1032192\)	\(1.6777\)	\(\Gamma_0(N)\)-optimal
169065.bc2	169065bh2	\([1, -1, 0, -184725, 22096800]\)	\(39616946929/10989225\)	\(193369565809944225\)	\([2, 2]\)	\(2064384\)	\(2.0243\)
169065.bc1	169065bh3	\([1, -1, 0, -2720700, 1727793585]\)	\(126574061279329/16286595\)	\(286583612918327595\)	\([2]\)	\(4128768\)	\(2.3709\)
169065.bc4	169065bh4	\([1, -1, 0, 478530, 144268371]\)	\(688699320191/910381875\)	\(-16019341481314006875\)	\([2]\)	\(4128768\)	\(2.3709\)

Rank

The elliptic curves in class 169065bh have rank \(1\).

Complex multiplication

The elliptic curves in class 169065bh do not have complex multiplication.

Modular form 169065.2.a.bh

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.