Elliptic curve isogeny class with LMFDB label 4002.a (Cremona label 4002c)

• Label: 4002.a
• Number of curves: $2$
• Conductor: $4002$
• CM: no
• Rank: $2$

Elliptic curves in class 4002.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4002.a1	4002c2	$[1, 1, 0, -3711, 85485]$	$5654307459987577/368184$	$368184$	$[2]$	$2688$	$0.52612$
4002.a2	4002c1	$[1, 1, 0, -231, 1269]$	$-1372441819897/11141568$	$-11141568$	$[2]$	$1344$	$0.17955$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 4002.a have rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$23$	$1 - T$
$29$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 2 T + 19 T^{2}$	1.19.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 4002.a do not have complex multiplication.

Modular form 4002.2.a.a

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.