Elliptic curve isogeny class with Cremona label 198744br (LMFDB label 198744.u)

• Label: 198744br
• Number of curves: $2$
• Conductor: $198744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 198744br have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 198744.2.a.br

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 198744br

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198744.u2	198744br1	\([0, -1, 0, -27603, 3721236]\)	\(-256000/507\)	\(-4606555372556592\)	\([2]\)	\(1032192\)	\(1.6950\)	\(\Gamma_0(N)\)-optimal
198744.u1	198744br2	\([0, -1, 0, -565868, 163908900]\)	\(137842000/117\)	\(17008819837132032\)	\([2]\)	\(2064384\)	\(2.0416\)