Elliptic curve isogeny class with Cremona label 20160dm (LMFDB label 20160.fd)

• Label: 20160dm
• Number of curves: $2$
• Conductor: $20160$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 20160dm have rank \(0\).

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.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 20160.2.a.dm

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 20160dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20160.fd1	20160dm1	\([0, 0, 0, -2951532, 1947510864]\)	\(551105805571803/1376829440\)	\(7104137492567162880\)	\([2]\)	\(645120\)	\(2.4946\)	\(\Gamma_0(N)\)-optimal
20160.fd2	20160dm2	\([0, 0, 0, -1845612, 3424577616]\)	\(-134745327251163/903920796800\)	\(-4664032767092824473600\)	\([2]\)	\(1290240\)	\(2.8412\)