Elliptic curve isogeny class with Cremona label 243936cx (LMFDB label 243936.cx)

• Label: 243936cx
• Number of curves: $4$
• Conductor: $243936$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 243936cx have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 243936cx do not have complex multiplication.

Modular form 243936.2.a.cx

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 243936cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
243936.cx3	243936cx1	\([0, 0, 0, -59169, -4525400]\)	\(277167808/53361\)	\(4410497426803776\)	\([2, 2]\)	\(1228800\)	\(1.7191\)	\(\Gamma_0(N)\)-optimal
243936.cx2	243936cx2	\([0, 0, 0, -287859, 55345642]\)	\(3989418056/307461\)	\(203302929006955008\)	\([2]\)	\(2457600\)	\(2.0656\)
243936.cx4	243936cx3	\([0, 0, 0, 120516, -26662592]\)	\(36594368/79233\)	\(-419130906983534592\)	\([2]\)	\(2457600\)	\(2.0656\)
243936.cx1	243936cx4	\([0, 0, 0, -897699, -327359450]\)	\(120993582536/6237\)	\(4124101489998336\)	\([2]\)	\(2457600\)	\(2.0656\)