Elliptic curve isogeny class with Cremona label 206310bg (LMFDB label 206310.bi)

• Label: 206310bg
• Number of curves: $6$
• Conductor: $206310$
• CM: no
• Rank: $0$

Elliptic curves in class 206310bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
206310.bi6	206310bg1	$[1, 1, 1, 7924, -105427]$	$371694959/249600$	$-36949757894400$	$[2]$	$720896$	$1.2921$	$\Gamma_0(N)$-optimal
206310.bi5	206310bg2	$[1, 1, 1, -34396, -917971]$	$30400540561/15210000$	$2251625871690000$	$[2, 2]$	$1441792$	$1.6387$
206310.bi3	206310bg3	$[1, 1, 1, -298896, 62138829]$	$19948814692561/231344100$	$34247229508404900$	$[2, 2]$	$2883584$	$1.9852$
206310.bi2	206310bg4	$[1, 1, 1, -447016, -115131187]$	$66730743078481/60937500$	$9020936985937500$	$[2]$	$2883584$	$1.9852$
206310.bi1	206310bg5	$[1, 1, 1, -4768946, 4006510949]$	$81025909800741361/11088090$	$1641435260462010$	$[2]$	$5767168$	$2.3318$
206310.bi4	206310bg6	$[1, 1, 1, -60846, 158691909]$	$-168288035761/73415764890$	$-10868168022106137210$	$[2]$	$5767168$	$2.3318$

Rank

The elliptic curves in class 206310bg have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 + T$
$5$	$1 + T$
$13$	$1 - T$
$23$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 3 T + 7 T^{2}$	1.7.d
$11$	$1 + 5 T + 11 T^{2}$	1.11.f
$17$	$1 - 4 T + 17 T^{2}$	1.17.ae
$19$	$1 + 4 T + 19 T^{2}$	1.19.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 206310bg do not have complex multiplication.

Modular form 206310.2.a.bg

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.