Elliptic curve isogeny class with Cremona label 198450id (LMFDB label 198450.r)

• Label: 198450id
• Number of curves: $2$
• Conductor: $198450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 198450id have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 198450id do not have complex multiplication.

Modular form 198450.2.a.id

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 198450id

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198450.r2	198450id1	\([1, -1, 0, -49842, 4167316]\)	\(1876833/64\)	\(466948881000000\)	\([]\)	\(979776\)	\(1.5868\)	\(\Gamma_0(N)\)-optimal
198450.r1	198450id2	\([1, -1, 0, -564342, -161673184]\)	\(415233/4\)	\(191478225515062500\)	\([]\)	\(2939328\)	\(2.1361\)