Elliptic curve isogeny class with Cremona label 4032bj (LMFDB label 4032.bk)

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

Rank

The elliptic curves in class 4032bj 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.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 4032.2.a.bj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 4032bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4032.bk4	4032bj1	\([0, 0, 0, 36, 432]\)	\(432/7\)	\(-83607552\)	\([2]\)	\(1024\)	\(0.20070\)	\(\Gamma_0(N)\)-optimal
4032.bk3	4032bj2	\([0, 0, 0, -684, 6480]\)	\(740772/49\)	\(2341011456\)	\([2, 2]\)	\(2048\)	\(0.54727\)
4032.bk2	4032bj3	\([0, 0, 0, -2124, -29808]\)	\(11090466/2401\)	\(229419122688\)	\([2]\)	\(4096\)	\(0.89385\)
4032.bk1	4032bj4	\([0, 0, 0, -10764, 429840]\)	\(1443468546/7\)	\(668860416\)	\([2]\)	\(4096\)	\(0.89385\)