Properties

Label 202800.n
Number of curves $4$
Conductor $202800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 202800.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202800.n1 202800je4 \([0, -1, 0, -35153408, -80211350688]\) \(31103978031362/195\) \(30119288160000000\) \([2]\) \(12386304\) \(2.7676\)  
202800.n2 202800je3 \([0, -1, 0, -3043408, -199990688]\) \(20183398562/11567205\) \(1786646054363040000000\) \([2]\) \(12386304\) \(2.7676\)  
202800.n3 202800je2 \([0, -1, 0, -2198408, -1251170688]\) \(15214885924/38025\) \(2936630595600000000\) \([2, 2]\) \(6193152\) \(2.4210\)  
202800.n4 202800je1 \([0, -1, 0, -85908, -34370688]\) \(-3631696/24375\) \(-470613877500000000\) \([2]\) \(3096576\) \(2.0744\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 202800.n have rank \(1\).

Complex multiplication

The elliptic curves in class 202800.n do not have complex multiplication.

Modular form 202800.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - 4q^{7} + q^{9} + 4q^{11} - 6q^{17} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().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.

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

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.