Elliptic curve isogeny class with LMFDB label 81144.bt (Cremona label 81144q)

• Label: 81144.bt
• Number of curves: $4$
• Conductor: $81144$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 81144.bt 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
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 81144.2.a.bt

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 81144.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
81144.bt1	81144q4	\([0, 0, 0, -331779, 62245582]\)	\(45989074372/7555707\)	\(663576249141808128\)	\([2]\)	\(884736\)	\(2.1413\)
81144.bt2	81144q2	\([0, 0, 0, -93639, -10101350]\)	\(4135597648/385641\)	\(8467182763151616\)	\([2, 2]\)	\(442368\)	\(1.7948\)
81144.bt3	81144q1	\([0, 0, 0, -91434, -10641575]\)	\(61604313088/621\)	\(852172178256\)	\([2]\)	\(221184\)	\(1.4482\)	\(\Gamma_0(N)\)-optimal
81144.bt4	81144q3	\([0, 0, 0, 109221, -47873882]\)	\(1640689628/12223143\)	\(-1073491519015222272\)	\([2]\)	\(884736\)	\(2.1413\)