Elliptic curve isogeny class with Cremona label 2160x (LMFDB label 2160.x)

• Label: 2160x
• Number of curves: $2$
• Conductor: $2160$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2160x have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2160x do not have complex multiplication.

Modular form 2160.2.a.x

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 2160x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2160.x2	2160x1	\([0, 0, 0, 3, -1]\)	\(6912/5\)	\(-2160\)	\([]\)	\(144\)	\(-0.67182\)	\(\Gamma_0(N)\)-optimal
2160.x1	2160x2	\([0, 0, 0, -57, -169]\)	\(-5267712/125\)	\(-486000\)	\([]\)	\(432\)	\(-0.12251\)