Elliptic curve isogeny class with Cremona label 168175bf (LMFDB label 168175.bf)

• Label: 168175bf
• Number of curves: $2$
• Conductor: $168175$
• CM: no
• Rank: $1$

Elliptic curves in class 168175bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
168175.bf2	168175bf1	\([0, -1, 1, 40042, 4296693]\)	\(4096/7\)	\(-12133839388671875\)	\([]\)	\(1224000\)	\(1.7712\)	\(\Gamma_0(N)\)-optimal
168175.bf1	168175bf2	\([0, -1, 1, -3563708, -2601214557]\)	\(-2887553024/16807\)	\(-29133348372201171875\)	\([]\)	\(6120000\)	\(2.5759\)

Rank

The elliptic curves in class 168175bf have rank \(1\).

Complex multiplication

The elliptic curves in class 168175bf do not have complex multiplication.

Modular form 168175.2.a.bf

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.