Elliptic curve isogeny class with Cremona label 244800bj (LMFDB label 244800.bj)

• Label: 244800bj
• Number of curves: $4$
• Conductor: $244800$
• CM: no
• Rank: $1$

Elliptic curves in class 244800bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
244800.bj4	244800bj1	$[0, 0, 0, -18212700, 908139854000]$	$-3579968623693264/1906997690433375$	$-355891536979438176000000000$	$[2]$	$82575360$	$3.7738$	$\Gamma_0(N)$-optimal
244800.bj3	244800bj2	$[0, 0, 0, -1521590700, 22607897906000]$	$521902963282042184836/6241849278890625$	$4659515519294736000000000000$	$[2, 2]$	$165150720$	$4.1204$
244800.bj1	244800bj3	$[0, 0, 0, -24275138700, 1455762872234000]$	$1059623036730633329075378/154307373046875$	$230379673500000000000000000$	$[2]$	$330301440$	$4.4670$
244800.bj2	244800bj4	$[0, 0, 0, -2822090700, -21762561094000]$	$1664865424893526702418/826424127435466125$	$1233844610868131440896000000000$	$[2]$	$330301440$	$4.4670$

Rank

The elliptic curves in class 244800bj have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1$
$17$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 244800bj do not have complex multiplication.

Modular form 244800.2.a.bj

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.