Elliptic curve isogeny class with Cremona label 51744bz (LMFDB label 51744.f)

• Label: 51744bz
• Number of curves: $1$
• Conductor: $51744$
• CM: no
• Rank: $1$

Rank

The elliptic curve 51744bz1 has rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51744bz do not have complex multiplication.

Modular form 51744.2.a.bz

Elliptic curves in class 51744bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51744.f1	51744bz1	\([0, -1, 0, -32909, 2671845]\)	\(-19639251778048/3874403907\)	\(-777608361750528\)	\([]\)	\(209664\)	\(1.5803\)	\(\Gamma_0(N)\)-optimal