Elliptic curve isogeny class with LMFDB label 228800.dl (Cremona label 228800ez)

• Label: 228800.dl
• Number of curves: $4$
• Conductor: $228800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 228800.dl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228800.dl do not have complex multiplication.

Modular form 228800.2.a.dl

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 228800.dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228800.dl1	228800ez3	\([0, 0, 0, -23624362700, 1397617294374000]\)	\(355995140004443961140387841/2768480\)	\(11339694080000000\)	\([2]\)	\(123863040\)	\(4.1026\)
228800.dl2	228800ez4	\([0, 0, 0, -1479850700, 21734381606000]\)	\(87501897507774086005761/815991377947460000\)	\(3342300684072796160000000000\)	\([2]\)	\(123863040\)	\(4.1026\)
228800.dl3	228800ez2	\([0, 0, 0, -1476522700, 21837769254000]\)	\(86912881496074271306241/7664481510400\)	\(31393716266598400000000\)	\([2, 2]\)	\(61931520\)	\(3.7561\)
228800.dl4	228800ez1	\([0, 0, 0, -92074700, 342829606000]\)	\(-21075830718885163521/199306463150080\)	\(-816359273062727680000000\)	\([2]\)	\(30965760\)	\(3.4095\)	\(\Gamma_0(N)\)-optimal