Elliptic curve isogeny class with LMFDB label 2880.bg (Cremona label 2880bg)

• Label: 2880.bg
• Number of curves: $4$
• Conductor: $2880$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2880.bg 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
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2880.bg do not have complex multiplication.

Modular form 2880.2.a.bg

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 2880.bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2880.bg1	2880bg3	\([0, 0, 0, -3852, -92016]\)	\(132304644/5\)	\(238878720\)	\([2]\)	\(2048\)	\(0.69367\)
2880.bg2	2880bg2	\([0, 0, 0, -252, -1296]\)	\(148176/25\)	\(298598400\)	\([2, 2]\)	\(1024\)	\(0.34709\)
2880.bg3	2880bg1	\([0, 0, 0, -72, 216]\)	\(55296/5\)	\(3732480\)	\([2]\)	\(512\)	\(0.00051877\)	\(\Gamma_0(N)\)-optimal
2880.bg4	2880bg4	\([0, 0, 0, 468, -7344]\)	\(237276/625\)	\(-29859840000\)	\([2]\)	\(2048\)	\(0.69367\)