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Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 286110a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.a1 286110a1 \([1, -1, 0, -730935, -287460059]\) \(-2454365649169/610929000\) \(-10750082509977129000\) \([]\) \(10948608\) \(2.3697\) \(\Gamma_0(N)\)-optimal
286110.a2 286110a2 \([1, -1, 0, 5277375, 2004109375]\) \(923754305147471/633316406250\) \(-11144017753470035156250\) \([]\) \(32845824\) \(2.9190\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 286110.2.a.a

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