Elliptic curve isogeny class with LMFDB label 23520.bu (Cremona label 23520bx)

• Label: 23520.bu
• Number of curves: $4$
• Conductor: $23520$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23520.bu have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 23520.bu do not have complex multiplication.

Modular form 23520.2.a.bu

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 23520.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23520.bu1	23520bx4	\([0, 1, 0, -176465, -28591137]\)	\(1261112198464/675\)	\(325275955200\)	\([2]\)	\(110592\)	\(1.5386\)
23520.bu2	23520bx3	\([0, 1, 0, -24320, 804600]\)	\(26410345352/10546875\)	\(635304600000000\)	\([2]\)	\(110592\)	\(1.5386\)
23520.bu3	23520bx1	\([0, 1, 0, -11090, -444312]\)	\(20034997696/455625\)	\(3430644840000\)	\([2, 2]\)	\(55296\)	\(1.1920\)	\(\Gamma_0(N)\)-optimal
23520.bu4	23520bx2	\([0, 1, 0, 1160, -1360612]\)	\(2863288/13286025\)	\(-800300828275200\)	\([2]\)	\(110592\)	\(1.5386\)