Elliptic curve isogeny class with Cremona label 382200k (LMFDB label 382200.k)

• Label: 382200k
• Number of curves: $4$
• Conductor: $382200$
• CM: no
• Rank: $0$

Elliptic curves in class 382200k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382200.k4	382200k1	$[0, -1, 0, 59617, -716988]$	$796706816/468195$	$-13770668388750000$	$[2]$	$2949120$	$1.7862$	$\Gamma_0(N)$-optimal
382200.k3	382200k2	$[0, -1, 0, -240508, -5518988]$	$3269383504/1863225$	$876826232100000000$	$[2, 2]$	$5898240$	$2.1327$
382200.k2	382200k3	$[0, -1, 0, -2470008, 1488246012]$	$885341342596/4606875$	$8671907790000000000$	$[2]$	$11796480$	$2.4793$
382200.k1	382200k4	$[0, -1, 0, -2813008, -1811413988]$	$1307761493476/2998905$	$5645090789520000000$	$[2]$	$11796480$	$2.4793$

Rank

The elliptic curves in class 382200k have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$5$	$1$
$7$	$1$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 - 8 T + 19 T^{2}$	1.19.ai
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 382200k do not have complex multiplication.

Modular form 382200.2.a.k

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.