Elliptic curve isogeny class with Cremona label 223440dx (LMFDB label 223440.dn)

• Label: 223440dx
• Number of curves: $2$
• Conductor: $223440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 223440dx have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	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 223440dx do not have complex multiplication.

Modular form 223440.2.a.dx

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 223440dx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
223440.dn2	223440dx1	\([0, -1, 0, -77240, 9091440]\)	\(-105756712489/12476160\)	\(-6012140535152640\)	\([2]\)	\(1658880\)	\(1.7635\)	\(\Gamma_0(N)\)-optimal
223440.dn1	223440dx2	\([0, -1, 0, -1268920, 550590832]\)	\(468898230633769/5540400\)	\(2669865040281600\)	\([2]\)	\(3317760\)	\(2.1101\)