Elliptic curve isogeny class with Cremona label 198550bk (LMFDB label 198550.db)

• Label: 198550bk
• Number of curves: $2$
• Conductor: $198550$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 198550bk have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198550bk do not have complex multiplication.

Modular form 198550.2.a.bk

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 198550bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198550.db2	198550bk1	\([1, 1, 1, 17862, -295219]\)	\(34295/22\)	\(-404300539843750\)	\([]\)	\(1137240\)	\(1.4917\)	\(\Gamma_0(N)\)-optimal
198550.db1	198550bk2	\([1, 1, 1, -207763, 42122281]\)	\(-53969305/10648\)	\(-195681461284375000\)	\([]\)	\(3411720\)	\(2.0410\)