Elliptic curve isogeny class with Cremona label 198198i (LMFDB label 198198.dj)

• Label: 198198i
• Number of curves: $2$
• Conductor: $198198$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 198198i have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198198i do not have complex multiplication.

Modular form 198198.2.a.i

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 198198i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198198.dj2	198198i1	\([1, -1, 1, -236336, 41856851]\)	\(849278123/52416\)	\(90100161718991424\)	\([2]\)	\(2433024\)	\(2.0050\)	\(\Gamma_0(N)\)-optimal
198198.dj1	198198i2	\([1, -1, 1, -715496, -181240045]\)	\(23565848363/5366088\)	\(9224004055981747032\)	\([2]\)	\(4866048\)	\(2.3516\)