Elliptic curve isogeny class with LMFDB label 4032.be (Cremona label 4032f)

• Label: 4032.be
• Number of curves: $4$
• Conductor: $4032$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 4032.be have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4032.be do not have complex multiplication.

Modular form 4032.2.a.be

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 4032.be

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4032.be1	4032f3	\([0, 0, 0, -5484, -156112]\)	\(381775972/567\)	\(27088846848\)	\([2]\)	\(4096\)	\(0.90284\)
4032.be2	4032f2	\([0, 0, 0, -444, -880]\)	\(810448/441\)	\(5267275776\)	\([2, 2]\)	\(2048\)	\(0.55626\)
4032.be3	4032f1	\([0, 0, 0, -264, 1640]\)	\(2725888/21\)	\(15676416\)	\([2]\)	\(1024\)	\(0.20969\)	\(\Gamma_0(N)\)-optimal
4032.be4	4032f4	\([0, 0, 0, 1716, -6928]\)	\(11696828/7203\)	\(-344128684032\)	\([2]\)	\(4096\)	\(0.90284\)