Elliptic curve isogeny class with Cremona label 106742g (LMFDB label 106742.k)

• Label: 106742g
• Number of curves: $3$
• Conductor: $106742$
• CM: no
• Rank: $0$

Elliptic curves in class 106742g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
106742.k2	106742g1	$[1, 1, 1, -43598, 3486819]$	$-413493625/152$	$-3368982891608$	$[]$	$302328$	$1.3717$	$\Gamma_0(N)$-optimal
106742.k3	106742g2	$[1, 1, 1, 26627, 13329555]$	$94196375/3511808$	$-77836980727711232$	$[]$	$906984$	$1.9210$
106742.k1	106742g3	$[1, 1, 1, -240228, -364643867]$	$-69173457625/2550136832$	$-56522153672812003328$	$[]$	$2720952$	$2.4703$

Rank

The elliptic curves in class 106742g have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$19$	$1 + T$
$53$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 - 3 T + 7 T^{2}$	1.7.ad
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 - T + 13 T^{2}$	1.13.ab
$17$	$1 - 5 T + 17 T^{2}$	1.17.af
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 7 T + 29 T^{2}$	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 106742g do not have complex multiplication.

Modular form 106742.2.a.g

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.