Elliptic curve isogeny class with LMFDB label 229320.bi (Cremona label 229320dx)

• Label: 229320.bi
• Number of curves: $4$
• Conductor: $229320$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 229320.bi have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 229320.bi do not have complex multiplication.

Modular form 229320.2.a.bi

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 229320.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
229320.bi1	229320dx3	\([0, 0, 0, -3394083, 2400956782]\)	\(49235161015876/137109375\)	\(12041563388400000000\)	\([2]\)	\(4718592\)	\(2.5338\)
229320.bi2	229320dx4	\([0, 0, 0, -3164763, -2158887962]\)	\(39914580075556/172718325\)	\(15168901899128140800\)	\([2]\)	\(4718592\)	\(2.5338\)
229320.bi3	229320dx2	\([0, 0, 0, -298263, 4172938]\)	\(133649126224/77000625\)	\(1690635499731360000\)	\([2, 2]\)	\(2359296\)	\(2.1872\)
229320.bi4	229320dx1	\([0, 0, 0, 74382, 521017]\)	\(33165879296/19278675\)	\(-26455314764314800\)	\([2]\)	\(1179648\)	\(1.8406\)	\(\Gamma_0(N)\)-optimal