Elliptic curve isogeny class with LMFDB label 198900.cn (Cremona label 198900cc)

• Label: 198900.cn
• Number of curves: $4$
• Conductor: $198900$
• CM: no
• Rank: $1$

Elliptic curves in class 198900.cn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
198900.cn1	198900cc3	$[0, 0, 0, -1114500, 61131125]$	$840033089536000/477272151837$	$86982849672293250000$	$[2]$	$4976640$	$2.5159$
198900.cn2	198900cc1	$[0, 0, 0, -709500, -230023375]$	$216727177216000/2738853$	$499155959250000$	$[2]$	$1658880$	$1.9666$	$\Gamma_0(N)$-optimal
198900.cn3	198900cc2	$[0, 0, 0, -690375, -243009250]$	$-12479332642000/1526829993$	$-4452236259588000000$	$[2]$	$3317760$	$2.3132$
198900.cn4	198900cc4	$[0, 0, 0, 4412625, 486719750]$	$3258571509326000/1920843121977$	$-5601178543684932000000$	$[2]$	$9953280$	$2.8625$

Rank

The elliptic curves in class 198900.cn have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1$
$13$	$1 + T$
$17$	$1 + T$

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 198900.cn do not have complex multiplication.

Modular form 198900.2.a.cn

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 LMFDB numbering.

$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.