Elliptic curve isogeny class with LMFDB label 168.a (Cremona label 168b)

• Label: 168.a
• Number of curves: $4$
• Conductor: $168$
• CM: no
• Rank: $0$

Elliptic curves in class 168.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
168.a1	168b4	$[0, -1, 0, -4032, 99900]$	$7080974546692/189$	$193536$	$[2]$	$96$	$0.52819$
168.a2	168b3	$[0, -1, 0, -392, -228]$	$6522128932/3720087$	$3809369088$	$[2]$	$96$	$0.52819$
168.a3	168b2	$[0, -1, 0, -252, 1620]$	$6940769488/35721$	$9144576$	$[2, 2]$	$48$	$0.18162$
168.a4	168b1	$[0, -1, 0, -7, 52]$	$-2725888/64827$	$-1037232$	$[4]$	$24$	$-0.16496$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 168.a have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$7$	$1 - T$

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
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 10 T + 29 T^{2}$	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 168.a do not have complex multiplication.

Modular form 168.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.