Elliptic curve isogeny class with LMFDB label 9702.s (Cremona label 9702a)

• Label: 9702.s
• Number of curves: $1$
• Conductor: $9702$
• CM: no
• Rank: $1$

Rank

The elliptic curve 9702.s1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9702.s do not have complex multiplication.

Modular form 9702.2.a.s

Elliptic curves in class 9702.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9702.s1	9702a1	\([1, -1, 0, -244176, -46392256]\)	\(-34068278205171/10307264\)	\(-487109783426112\)	\([]\)	\(60480\)	\(1.7959\)	\(\Gamma_0(N)\)-optimal