Elliptic curve isogeny class with Cremona label 98553g (LMFDB label 98553.x)

• Label: 98553g
• Number of curves: $2$
• Conductor: $98553$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 98553g have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 98553g do not have complex multiplication.

Modular form 98553.2.a.g

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 98553g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98553.x1	98553g1	\([1, 1, 0, -9754, -19505]\)	\(2181825073/1260441\)	\(59298557293521\)	\([2]\)	\(276480\)	\(1.3323\)	\(\Gamma_0(N)\)-optimal
98553.x2	98553g2	\([1, 1, 0, 38981, -107228]\)	\(139233463487/80714907\)	\(-3797303909648067\)	\([2]\)	\(552960\)	\(1.6789\)