Elliptic curve isogeny class with LMFDB label 44100.dt (Cremona label 44100cn)

• Label: 44100.dt
• Number of curves: $4$
• Conductor: $44100$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 44100.dt have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 44100.dt do not have complex multiplication.

Modular form 44100.2.a.dt

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 44100.dt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
44100.dt1	44100cn4	\([0, 0, 0, -20157375, -34833622250]\)	\(2640279346000/3087\)	\(1059040062108000000\)	\([2]\)	\(1990656\)	\(2.7418\)
44100.dt2	44100cn3	\([0, 0, 0, -1249500, -553644875]\)	\(-10061824000/352947\)	\(-7567723777146750000\)	\([2]\)	\(995328\)	\(2.3952\)
44100.dt3	44100cn2	\([0, 0, 0, -312375, -21523250]\)	\(9826000/5103\)	\(1750658061852000000\)	\([2]\)	\(663552\)	\(2.1925\)
44100.dt4	44100cn1	\([0, 0, 0, 73500, -2615375]\)	\(2048000/1323\)	\(-28367144520750000\)	\([2]\)	\(331776\)	\(1.8459\)	\(\Gamma_0(N)\)-optimal