Elliptic curve isogeny class with LMFDB label 144.a (Cremona label 144a)

• Label: 144.a
• Number of curves: $4$
• Conductor: $144$
• CM: \(\Q(\sqrt{-3}) \)
• Rank: $0$

Rank

The elliptic curves in class 144.a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 144.a has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-3}) \).

Modular form 144.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 144.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
144.a1	144a4	\([0, 0, 0, -135, 594]\)	\(54000\)	\(5038848\)	\([2]\)	\(24\)	\(0.080464\)		\(-12\)
144.a2	144a2	\([0, 0, 0, -15, -22]\)	\(54000\)	\(6912\)	\([2]\)	\(8\)	\(-0.46884\)		\(-12\)
144.a3	144a1	\([0, 0, 0, 0, -1]\)	\(0\)	\(-432\)	\([2]\)	\(4\)	\(-0.81542\)	\(\Gamma_0(N)\)-optimal	\(-3\)
144.a4	144a3	\([0, 0, 0, 0, 27]\)	\(0\)	\(-314928\)	\([2]\)	\(12\)	\(-0.26611\)		\(-3\)