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

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

Rank

The elliptic curves in class 81144bz 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 81144.2.a.bz

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 81144bz

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	\([0, 0, 0, 861, 14798]\)	\(275684/529\)	\(-135449459712\)	\([2]\)	\(73728\)	\(0.82058\)