Elliptic curve isogeny class with LMFDB label 81144.bs (Cremona label 81144bz)

• Label: 81144.bs
• Number of curves: $2$
• Conductor: $81144$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 81144.bs have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 81144.bs do not have complex multiplication.

Modular form 81144.2.a.bs

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 81144.bs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81144.bs1	81144bz1	\([0, 0, 0, -399, 2450]\)	\(109744/23\)	\(1472276736\)	\([2]\)	\(36864\)	\(0.47400\)	\(\Gamma_0(N)\)-optimal
81144.bs2	81144bz2	\([0, 0, 0, 861, 14798]\)	\(275684/529\)	\(-135449459712\)	\([2]\)	\(73728\)	\(0.82058\)