Elliptic curve isogeny class with LMFDB label 223440.bt (Cremona label 223440fg)

• Label: 223440.bt
• Number of curves: $4$
• Conductor: $223440$
• CM: no
• Rank: $1$

Rank

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

See L-function page for more information

Complex multiplication

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

Modular form 223440.2.a.bt

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 223440.bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
223440.bt1	223440fg4	\([0, -1, 0, -9834501896, -375381507064080]\)	\(218289391029690300712901881/306514992000\)	\(147706602675437568000\)	\([2]\)	\(123863040\)	\(4.0350\)
223440.bt2	223440fg3	\([0, -1, 0, -643262216, -5289267085584]\)	\(61085713691774408830201/10268551781250000000\)	\(4948315539506304000000000000\)	\([2]\)	\(123863040\)	\(4.0350\)
223440.bt3	223440fg2	\([0, -1, 0, -614661896, -5865071608080]\)	\(53294746224000958661881/1997017344000000\)	\(962343294993432576000000\)	\([2, 2]\)	\(61931520\)	\(3.6885\)
223440.bt4	223440fg1	\([0, -1, 0, -36634376, -100518756624]\)	\(-11283450590382195961/2530373271552000\)	\(-1219362345061667831808000\)	\([2]\)	\(30965760\)	\(3.3419\)	\(\Gamma_0(N)\)-optimal