Elliptic curve isogeny class with LMFDB label 304704.dz (Cremona label 304704dz)

• Label: 304704.dz
• Number of curves: $1$
• Conductor: $304704$
• CM: no
• Rank: $1$

Rank

The elliptic curve 304704.dz1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 3 T + 13 T^{2}\)	1.13.ad
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 304704.dz do not have complex multiplication.

Modular form 304704.2.a.dz

Elliptic curves in class 304704.dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
304704.dz1	304704dz1	\([0, 0, 0, -1715547, -865268372]\)	\(-152827456/81\)	\(-295947863670897216\)	\([]\)	\(3956736\)	\(2.3023\)	\(\Gamma_0(N)\)-optimal