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Properties

Label 286110v
Number of curves $2$
Conductor $286110$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 286110v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.v2 286110v1 \([1, -1, 0, -1593855, -773928999]\) \(125024751633535937/32226562500\) \(115421915039062500\) \([2]\) \(6488064\) \(2.2596\) \(\Gamma_0(N)\)-optimal
286110.v1 286110v2 \([1, -1, 0, -25500105, -49557022749]\) \(512006336026136035937/34031250\) \(121885542281250\) \([2]\) \(12976128\) \(2.6061\)  

Rank

sage: E.rank()
 

The elliptic curves in class 286110v have rank \(1\).

Complex multiplication

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

Modular form 286110.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} - 4 q^{13} + q^{16} + 6 q^{19} + O(q^{20})\) 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.