Elliptic curve isogeny class with Cremona label 98553r (LMFDB label 98553.a)

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

Rank

The elliptic curve 98553r1 has rank \(2\).

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.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 98553.2.a.r

Elliptic curves in class 98553r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
98553.a1	98553r1	\([0, -1, 1, -5174, 221276]\)	\(-325660672/254163\)	\(-11957322252603\)	\([]\)	\(259200\)	\(1.2080\)	\(\Gamma_0(N)\)-optimal