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Properties

Label 2286f
Number of curves $2$
Conductor $2286$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 2286f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2286.f2 2286f1 \([1, -1, 0, -917514, -334851084]\) \(117174888570509216929/1273887851544576\) \(928664243775995904\) \([]\) \(29568\) \(2.2628\) \(\Gamma_0(N)\)-optimal
2286.f1 2286f2 \([1, -1, 0, -201249954, 1098934153596]\) \(1236526859255318155975783969/38367061931916216\) \(27969588148366921464\) \([]\) \(206976\) \(3.2358\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2286f have rank \(1\).

Complex multiplication

The elliptic curves in class 2286f do not have complex multiplication.

Modular form 2286.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} - 5 q^{11} - q^{14} + q^{16} + 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.