Elliptic curve isogeny class with Cremona label 1323i (LMFDB label 1323.s)

• Label: 1323i
• Number of curves: $1$
• Conductor: $1323$
• CM: no
• Rank: $0$

Rank

The elliptic curve 1323i1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1323i do not have complex multiplication.

Modular form 1323.2.a.i

Elliptic curves in class 1323i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1323.s1	1323i1	\([0, 0, 1, -21, -37]\)	\(110592\)	\(9261\)	\([]\)	\(192\)	\(-0.41635\)	\(\Gamma_0(N)\)-optimal