Elliptic curve isogeny class with Cremona label 163170ba (LMFDB label 163170.ds)

• Label: 163170ba
• Number of curves: $3$
• Conductor: $163170$
• CM: no
• Rank: $1$

Elliptic curves in class 163170ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
163170.ds1	163170ba1	$[1, -1, 1, -23603, 1401621]$	$-16954786009/370$	$-31733464770$	$[]$	$326592$	$1.1310$	$\Gamma_0(N)$-optimal
163170.ds2	163170ba2	$[1, -1, 1, -8168, 3185907]$	$-702595369/50653000$	$-4344311327013000$	$[]$	$979776$	$1.6804$
163170.ds3	163170ba3	$[1, -1, 1, 73417, -85382769]$	$510273943271/37000000000$	$-3173346477000000000$	$[]$	$2939328$	$2.2297$

Rank

The elliptic curves in class 163170ba have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1$
$5$	$1 + T$
$7$	$1$
$37$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - T + 11 T^{2}$	1.11.ab
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 - T + 19 T^{2}$	1.19.ab
$23$	$1 + T + 23 T^{2}$	1.23.b
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 163170ba do not have complex multiplication.

Modular form 163170.2.a.ba

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.