Elliptic curve isogeny class with LMFDB label 44.a (Cremona label 44a)

• Label: 44.a
• Number of curves: $2$
• Conductor: $44$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44.a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 44.a do not have complex multiplication.

Modular form 44.2.a.a

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 44.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44.a1	44a2	\([0, 1, 0, -77, -289]\)	\(-199794688/1331\)	\(-340736\)	\([]\)	\(6\)	\(-0.10299\)
44.a2	44a1	\([0, 1, 0, 3, -1]\)	\(8192/11\)	\(-2816\)	\([3]\)	\(2\)	\(-0.65229\)	\(\Gamma_0(N)\)-optimal