Elliptic curve isogeny class with LMFDB label 44352.ds (Cremona label 44352x)

• Label: 44352.ds
• Number of curves: $4$
• Conductor: $44352$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44352.ds have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 44352.ds do not have complex multiplication.

Modular form 44352.2.a.ds

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 44352.ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44352.ds1	44352x4	\([0, 0, 0, -2974284, 1974338928]\)	\(15226621995131793/2324168\)	\(444155421523968\)	\([2]\)	\(589824\)	\(2.2162\)
44352.ds2	44352x3	\([0, 0, 0, -347724, -30306960]\)	\(24331017010833/12004097336\)	\(2294018725103271936\)	\([2]\)	\(589824\)	\(2.2162\)
44352.ds3	44352x2	\([0, 0, 0, -186444, 30656880]\)	\(3750606459153/45914176\)	\(8774335674187776\)	\([2, 2]\)	\(294912\)	\(1.8696\)
44352.ds4	44352x1	\([0, 0, 0, -2124, 1239408]\)	\(-5545233/3469312\)	\(-662995847872512\)	\([2]\)	\(147456\)	\(1.5231\)	\(\Gamma_0(N)\)-optimal