Elliptic curve isogeny class with LMFDB label 3168.i (Cremona label 3168l)

• Label: 3168.i
• Number of curves: $1$
• Conductor: $3168$
• CM: no
• Rank: $1$

Rank

The elliptic curve 3168.i1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 3168.i do not have complex multiplication.

Modular form 3168.2.a.i

Elliptic curves in class 3168.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3168.i1	3168l1	\([0, 0, 0, 72, 3024]\)	\(13824/1331\)	\(-3974344704\)	\([]\)	\(1344\)	\(0.52137\)	\(\Gamma_0(N)\)-optimal