Elliptic curve isogeny class with Cremona label 217800cu (LMFDB label 217800.hc)

• Label: 217800cu
• Number of curves: $4$
• Conductor: $217800$
• CM: no
• Rank: $0$

Elliptic curves in class 217800cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
217800.hc3	217800cu1	$[0, 0, 0, -137268450, 619019317125]$	$885956203616256/15125$	$4883363257781250000$	$[2]$	$26542080$	$3.1279$	$\Gamma_0(N)$-optimal
217800.hc2	217800cu2	$[0, 0, 0, -137404575, 617730077250]$	$55537159171536/228765625$	$1181773908383062500000000$	$[2, 2]$	$53084160$	$3.4745$
217800.hc4	217800cu3	$[0, 0, 0, -71520075, 1211283537750]$	$-1957960715364/29541015625$	$-610420407222656250000000000$	$[2]$	$106168320$	$3.8211$
217800.hc1	217800cu4	$[0, 0, 0, -205467075, -58334735250]$	$46424454082884/26794860125$	$553675257364365378000000000$	$[2]$	$106168320$	$3.8211$

Rank

The elliptic curves in class 217800cu have rank $0$.

Complex multiplication

The elliptic curves in class 217800cu do not have complex multiplication.

Modular form 217800.2.a.cu

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.