Elliptic curve isogeny class with LMFDB label 198744.bb (Cremona label 198744ds)

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

Rank

The elliptic curves in class 198744.bb 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 198744.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 198744.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198744.bb1	198744ds4	\([0, -1, 0, -448766712, 557104816332]\)	\(8594236719188066/4858291807551\)	\(5650175047579451977649338368\)	\([2]\)	\(130056192\)	\(4.0151\)
198744.bb2	198744ds2	\([0, -1, 0, -332501472, 2329591653180]\)	\(6991270724335972/14494474449\)	\(8428509556818959974818816\)	\([2, 2]\)	\(65028096\)	\(3.6685\)
198744.bb3	198744ds1	\([0, -1, 0, -332335852, 2332032163252]\)	\(27923315228972368/120393\)	\(17502075612408860928\)	\([2]\)	\(32514048\)	\(3.3220\)	\(\Gamma_0(N)\)-optimal
198744.bb4	198744ds3	\([0, -1, 0, -218886152, 3945883195500]\)	\(-997241325462146/5206220835543\)	\(-6054815194808470483135002624\)	\([2]\)	\(130056192\)	\(4.0151\)