Elliptic curve isogeny class with Cremona label 223440gs (LMFDB label 223440.fa)

• Label: 223440gs
• Number of curves: $4$
• Conductor: $223440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 223440gs 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 223440.2.a.gs

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 223440gs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
223440.fa4	223440gs1	\([0, 1, 0, 4884, -9780]\)	\(427694384/249375\)	\(-7510712160000\)	\([2]\)	\(442368\)	\(1.1600\)	\(\Gamma_0(N)\)-optimal
223440.fa3	223440gs2	\([0, 1, 0, -19616, -97980]\)	\(6929294404/3980025\)	\(479483864294400\)	\([2, 2]\)	\(884736\)	\(1.5066\)
223440.fa2	223440gs3	\([0, 1, 0, -205816, 35726900]\)	\(4001704635602/18475695\)	\(4451629140080640\)	\([2]\)	\(1769472\)	\(1.8532\)
223440.fa1	223440gs4	\([0, 1, 0, -225416, -41175660]\)	\(5257286722802/13683705\)	\(3297022381148160\)	\([2]\)	\(1769472\)	\(1.8532\)