Elliptic curve isogeny class with LMFDB label 51744.r (Cremona label 51744p)

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

Rank

The elliptic curve 51744.r1 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
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 51744.2.a.r

Elliptic curves in class 51744.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51744.r1	51744p1	\([0, -1, 0, -743633, -918227967]\)	\(-226591821421000000/1684650343696353\)	\(-338116062581232832512\)	\([]\)	\(1128960\)	\(2.6222\)	\(\Gamma_0(N)\)-optimal