Properties

Label 229320dr
Number of curves $2$
Conductor $229320$
CM no
Rank $2$
Graph

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

Elliptic curves in class 229320dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.o2 229320dr1 \([0, 0, 0, -187383, 29634122]\) \(11367178023472/651619215\) \(41711470042394880\) \([2]\) \(1916928\) \(1.9433\) \(\Gamma_0(N)\)-optimal
229320.o1 229320dr2 \([0, 0, 0, -2955603, 1955761598]\) \(11151682683009628/40040325\) \(10252250260761600\) \([2]\) \(3833856\) \(2.2899\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320dr have rank \(2\).

Complex multiplication

The elliptic curves in class 229320dr do not have complex multiplication.

Modular form 229320.2.a.dr

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4q^{11} + q^{13} + 2q^{19} + O(q^{20})\)  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.