Properties

Label 162288.dr
Number of curves $2$
Conductor $162288$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 162288.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.dr1 162288bp2 \([0, 0, 0, -4272555, -3182362918]\) \(24553362849625/1755162752\) \(616585219943321567232\) \([2]\) \(6193152\) \(2.7362\)  
162288.dr2 162288bp1 \([0, 0, 0, 243285, -217262374]\) \(4533086375/60669952\) \(-21313234715837202432\) \([2]\) \(3096576\) \(2.3896\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 162288.dr have rank \(0\).

Complex multiplication

The elliptic curves in class 162288.dr do not have complex multiplication.

Modular form 162288.2.a.dr

sage: E.q_eigenform(10)
 
\(q + 4q^{11} + 6q^{17} - 6q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.