Elliptic curve isogeny class with LMFDB label 11200.cz (Cremona label 11200co)

• Label: 11200.cz
• Number of curves: $6$
• Conductor: $11200$
• CM: no
• Rank: $1$

Elliptic curves in class 11200.cz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11200.cz1	11200co6	$[0, -1, 0, -4368833, 3516221537]$	$2251439055699625/25088$	$102760448000000$	$[2]$	$165888$	$2.2575$
11200.cz2	11200co5	$[0, -1, 0, -272833, 55101537]$	$-548347731625/1835008$	$-7516192768000000$	$[2]$	$82944$	$1.9110$
11200.cz3	11200co4	$[0, -1, 0, -56833, 4293537]$	$4956477625/941192$	$3855122432000000$	$[2]$	$55296$	$1.7082$
11200.cz4	11200co2	$[0, -1, 0, -16833, -834463]$	$128787625/98$	$401408000000$	$[2]$	$18432$	$1.1589$
11200.cz5	11200co1	$[0, -1, 0, -833, -18463]$	$-15625/28$	$-114688000000$	$[2]$	$9216$	$0.81236$	$\Gamma_0(N)$-optimal
11200.cz6	11200co3	$[0, -1, 0, 7167, 389537]$	$9938375/21952$	$-89915392000000$	$[2]$	$27648$	$1.3617$

Rank

The elliptic curves in class 11200.cz have rank $1$.

Complex multiplication

The elliptic curves in class 11200.cz do not have complex multiplication.

Modular form 11200.2.a.cz

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.

$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.