Elliptic curve isogeny class with LMFDB label 4032.j (Cremona label 4032d)

• Label: 4032.j
• Number of curves: $2$
• Conductor: $4032$
• CM: no
• Rank: $0$

Elliptic curves in class 4032.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4032.j1	4032d1	$[0, 0, 0, -216, -1080]$	$55296/7$	$141087744$	$[2]$	$1536$	$0.29296$	$\Gamma_0(N)$-optimal
4032.j2	4032d2	$[0, 0, 0, 324, -5616]$	$11664/49$	$-15801827328$	$[2]$	$3072$	$0.63953$

Rank

The elliptic curves in class 4032.j 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.c
$11$	$1 + 6 T + 11 T^{2}$	1.11.g
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 2 T + 23 T^{2}$	1.23.ac
$29$	$1 + 8 T + 29 T^{2}$	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 4032.2.a.j

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.