Elliptic curve isogeny class with LMFDB label 27048.v (Cremona label 27048w)

• Label: 27048.v
• Number of curves: $1$
• Conductor: $27048$
• CM: no
• Rank: $1$

Rank

The elliptic curve 27048.v1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27048.v do not have complex multiplication.

Modular form 27048.2.a.v

Elliptic curves in class 27048.v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27048.v1	27048w1	\([0, 1, 0, -464, 3744]\)	\(-110328386/1587\)	\(-159258624\)	\([]\)	\(11904\)	\(0.37870\)	\(\Gamma_0(N)\)-optimal