Elliptic curve isogeny class with LMFDB label 20160.bw (Cremona label 20160bm)

• Label: 20160.bw
• Number of curves: $4$
• Conductor: $20160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 20160.bw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20160.bw do not have complex multiplication.

Modular form 20160.2.a.bw

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.

Elliptic curves in class 20160.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20160.bw1	20160bm3	\([0, 0, 0, -23628, -1395088]\)	\(15267472418/36015\)	\(3441286840320\)	\([2]\)	\(32768\)	\(1.2855\)
20160.bw2	20160bm2	\([0, 0, 0, -2028, -4048]\)	\(19307236/11025\)	\(526727577600\)	\([2, 2]\)	\(16384\)	\(0.93893\)
20160.bw3	20160bm1	\([0, 0, 0, -1308, 18128]\)	\(20720464/105\)	\(1254113280\)	\([2]\)	\(8192\)	\(0.59236\)	\(\Gamma_0(N)\)-optimal
20160.bw4	20160bm4	\([0, 0, 0, 8052, -32272]\)	\(604223422/354375\)	\(-33861058560000\)	\([2]\)	\(32768\)	\(1.2855\)