Elliptic curve isogeny class with LMFDB label 16170.bi (Cremona label 16170bk)

• Label: 16170.bi
• Number of curves: $4$
• Conductor: $16170$
• CM: no
• Rank: $1$

Elliptic curves in class 16170.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16170.bi1	16170bk3	\([1, 1, 1, -2414721, 1443264423]\)	\(13235378341603461121/9240\)	\(1087076760\)	\([2]\)	\(147456\)	\(1.9469\)
16170.bi2	16170bk2	\([1, 1, 1, -150921, 22503543]\)	\(3231355012744321/85377600\)	\(10044589262400\)	\([2, 2]\)	\(73728\)	\(1.6003\)
16170.bi3	16170bk4	\([1, 1, 1, -145041, 24345159]\)	\(-2868190647517441/527295615000\)	\(-62035801809135000\)	\([2]\)	\(147456\)	\(1.9469\)
16170.bi4	16170bk1	\([1, 1, 1, -9801, 319479]\)	\(885012508801/127733760\)	\(15027749130240\)	\([2]\)	\(36864\)	\(1.2538\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 16170.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 16170.bi do not have complex multiplication.

Modular form 16170.2.a.bi

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.