Properties

Label 142800ds
Number of curves $2$
Conductor $142800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ds1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142800ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142800.dh2 142800ds1 \([0, -1, 0, 32592, -2714688]\) \(59822347031/83966400\) \(-5373849600000000\) \([2]\) \(663552\) \(1.7040\) \(\Gamma_0(N)\)-optimal
142800.dh1 142800ds2 \([0, -1, 0, -207408, -26714688]\) \(15417797707369/4080067320\) \(261124308480000000\) \([2]\) \(1327104\) \(2.0506\)  

Rank

sage: E.rank()
 

The elliptic curves in class 142800ds have rank \(1\).

Complex multiplication

The elliptic curves in class 142800ds do not have complex multiplication.

Modular form 142800.2.a.ds

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} - 2q^{11} + 2q^{13} - q^{17} + 4q^{19} + O(q^{20})\)  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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.