Elliptic curve isogeny class with Cremona label 54080cw (LMFDB label 54080.bs)

• Label: 54080cw
• Number of curves: $4$
• Conductor: $54080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 54080cw have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54080cw do not have complex multiplication.

Modular form 54080.2.a.cw

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 54080cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54080.bs3	54080cw1	\([0, 0, 0, -1352, -17576]\)	\(55296/5\)	\(24713262080\)	\([2]\)	\(36864\)	\(0.73369\)	\(\Gamma_0(N)\)-optimal
54080.bs2	54080cw2	\([0, 0, 0, -4732, 105456]\)	\(148176/25\)	\(1977060966400\)	\([2, 2]\)	\(73728\)	\(1.0803\)
54080.bs4	54080cw3	\([0, 0, 0, 8788, 597584]\)	\(237276/625\)	\(-197706096640000\)	\([2]\)	\(147456\)	\(1.4268\)
54080.bs1	54080cw4	\([0, 0, 0, -72332, 7487376]\)	\(132304644/5\)	\(1581648773120\)	\([2]\)	\(147456\)	\(1.4268\)