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Properties

Label 286110x
Number of curves $2$
Conductor $286110$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 286110x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.x2 286110x1 \([1, -1, 0, -377524800, 2830509690880]\) \(-338173143620095981729/979226371031040\) \(-17230749046990988944343040\) \([]\) \(104509440\) \(3.7134\) \(\Gamma_0(N)\)-optimal
286110.x1 286110x2 \([1, -1, 0, -30600728640, 2060380247097856]\) \(-180093466903641160790448289/4344384000\) \(-76445031182059584000\) \([]\) \(313528320\) \(4.2627\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 286110.2.a.x

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.