Elliptic curve isogeny class with LMFDB label 20160.dq (Cremona label 20160by)

• Label: 20160.dq
• Number of curves: $2$
• Conductor: $20160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 20160.dq 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 20160.2.a.dq

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 20160.dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20160.dq1	20160by1	\([0, 0, 0, -192, -376]\)	\(1048576/525\)	\(391910400\)	\([2]\)	\(6144\)	\(0.34167\)	\(\Gamma_0(N)\)-optimal
20160.dq2	20160by2	\([0, 0, 0, 708, -2896]\)	\(3286064/2205\)	\(-26336378880\)	\([2]\)	\(12288\)	\(0.68824\)