Elliptic curve isogeny class with LMFDB label 23232.cg (Cremona label 23232ch)

• Label: 23232.cg
• Number of curves: $4$
• Conductor: $23232$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23232.cg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 23232.cg do not have complex multiplication.

Modular form 23232.2.a.cg

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 23232.cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23232.cg1	23232ch4	\([0, 1, 0, -15649, 748031]\)	\(7301384/3\)	\(174151532544\)	\([2]\)	\(40960\)	\(1.1193\)
23232.cg2	23232ch2	\([0, 1, 0, -1129, 7511]\)	\(21952/9\)	\(65306824704\)	\([2, 2]\)	\(20480\)	\(0.77273\)
23232.cg3	23232ch1	\([0, 1, 0, -524, -4710]\)	\(140608/3\)	\(340139712\)	\([2]\)	\(10240\)	\(0.42615\)	\(\Gamma_0(N)\)-optimal
23232.cg4	23232ch3	\([0, 1, 0, 3711, 58815]\)	\(97336/81\)	\(-4702091378688\)	\([2]\)	\(40960\)	\(1.1193\)