Elliptic curve isogeny class with Cremona label 16562bm (LMFDB label 16562.bd)

• Label: 16562bm
• Number of curves: $3$
• Conductor: $16562$
• CM: no
• Rank: $1$

Elliptic curves in class 16562bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
16562.bd3	16562bm1	$[1, 1, 1, 3968, -156213]$	$12167/26$	$-14764600553066$	$[]$	$42336$	$1.2112$	$\Gamma_0(N)$-optimal
16562.bd2	16562bm2	$[1, 1, 1, -37437, 5541115]$	$-10218313/17576$	$-9980869973872616$	$[]$	$127008$	$1.7605$
16562.bd1	16562bm3	$[1, 1, 1, -3805292, 2855546637]$	$-10730978619193/6656$	$-3779737741584896$	$[]$	$381024$	$2.3098$

Rank

The elliptic curves in class 16562bm have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$7$	$1$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 - T + 5 T^{2}$	1.5.ab
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + T + 29 T^{2}$	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 16562bm do not have complex multiplication.

Modular form 16562.2.a.bm

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.