Elliptic curve isogeny class with Cremona label 23232bl (LMFDB label 23232.dw)

• Label: 23232bl
• Number of curves: $2$
• Conductor: $23232$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 23232bl have rank \(0\).

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.ac
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 23232bl do not have complex multiplication.

Modular form 23232.2.a.bl

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 23232bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23232.dw2	23232bl1	\([0, 1, 0, -3681, -86913]\)	\(63253004/243\)	\(21196505088\)	\([2]\)	\(46080\)	\(0.83986\)	\(\Gamma_0(N)\)-optimal
23232.dw1	23232bl2	\([0, 1, 0, -5441, 2847]\)	\(102129622/59049\)	\(10301501472768\)	\([2]\)	\(92160\)	\(1.1864\)