Elliptic curve isogeny class with Cremona label 51744ct (LMFDB label 51744.bk)

• Label: 51744ct
• Number of curves: $2$
• Conductor: $51744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 51744ct have 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 51744.2.a.ct

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 51744ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51744.bk2	51744ct1	\([0, 1, 0, 670, 9624]\)	\(4410944/7623\)	\(-57397652928\)	\([2]\)	\(61440\)	\(0.74936\)	\(\Gamma_0(N)\)-optimal
51744.bk1	51744ct2	\([0, 1, 0, -4720, 95864]\)	\(193100552/43659\)	\(2629856097792\)	\([2]\)	\(122880\)	\(1.0959\)