Properties

Label 286110dr
Number of curves $2$
Conductor $286110$
CM no
Rank $0$
Graph

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

Elliptic curves in class 286110dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.dr1 286110dr1 \([1, -1, 1, -230243, 36031007]\) \(76711450249/12622500\) \(222109142768122500\) \([2]\) \(4423680\) \(2.0501\) \(\Gamma_0(N)\)-optimal
286110.dr2 286110dr2 \([1, -1, 1, 420007, 202234907]\) \(465664585751/1274620050\) \(-22428581236725010050\) \([2]\) \(8847360\) \(2.3967\)  

Rank

sage: E.rank()
 

The elliptic curves in class 286110dr have rank \(0\).

Complex multiplication

The elliptic curves in class 286110dr do not have complex multiplication.

Modular form 286110.2.a.dr

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - q^{10} + q^{11} - 4 q^{13} - 4 q^{14} + q^{16} + 4 q^{19} + O(q^{20})\) Copy content 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.