Elliptic curve isogeny class with Cremona label 23520bp (LMFDB label 23520.bf)

• Label: 23520bp
• Number of curves: $4$
• Conductor: $23520$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 23520bp have rank \(0\).

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.e
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 23520.2.a.bp

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 23520bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23520.bf3	23520bp1	\([0, 1, 0, -1486, -21736]\)	\(48228544/2025\)	\(15247310400\)	\([2, 2]\)	\(18432\)	\(0.71870\)	\(\Gamma_0(N)\)-optimal
23520.bf4	23520bp2	\([0, 1, 0, 719, -78625]\)	\(85184/5625\)	\(-2710632960000\)	\([2]\)	\(36864\)	\(1.0653\)
23520.bf2	23520bp3	\([0, 1, 0, -3936, 65484]\)	\(111980168/32805\)	\(1976051427840\)	\([2]\)	\(36864\)	\(1.0653\)
23520.bf1	23520bp4	\([0, 1, 0, -23536, -1397656]\)	\(23937672968/45\)	\(2710632960\)	\([2]\)	\(36864\)	\(1.0653\)