Elliptic curve isogeny class with Cremona label 223440de (LMFDB label 223440.ck)

• Label: 223440de
• Number of curves: $2$
• Conductor: $223440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 223440de have rank \(1\).

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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 223440de do not have complex multiplication.

Modular form 223440.2.a.de

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 223440de

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
223440.ck2	223440de1	\([0, -1, 0, -61560, -20600208]\)	\(-53540005609/350208000\)	\(-168761839583232000\)	\([2]\)	\(2903040\)	\(1.9890\)	\(\Gamma_0(N)\)-optimal
223440.ck1	223440de2	\([0, -1, 0, -1566840, -752768400]\)	\(882774443450089/2166000000\)	\(1043774398464000000\)	\([2]\)	\(5806080\)	\(2.3356\)