Elliptic curve isogeny class with Cremona label 198744dt (LMFDB label 198744.be)

• Label: 198744dt
• Number of curves: $4$
• Conductor: $198744$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 198744dt have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198744dt do not have complex multiplication.

Modular form 198744.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 198744dt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198744.be3	198744dt1	\([0, -1, 0, -60727, -3301052]\)	\(2725888/1053\)	\(9567461158386768\)	\([2]\)	\(1032192\)	\(1.7654\)	\(\Gamma_0(N)\)-optimal
198744.be2	198744dt2	\([0, -1, 0, -433372, 107598100]\)	\(61918288/1521\)	\(221114657882716416\)	\([2, 2]\)	\(2064384\)	\(2.1120\)
198744.be1	198744dt3	\([0, -1, 0, -6892552, 6967247260]\)	\(62275269892/39\)	\(22678426449509376\)	\([2]\)	\(4128768\)	\(2.4586\)
198744.be4	198744dt4	\([0, -1, 0, 63488, 339532348]\)	\(48668/85683\)	\(-49824502909572099072\)	\([2]\)	\(4128768\)	\(2.4586\)