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Properties

Label 286110fw
Number of curves $2$
Conductor $286110$
CM no
Rank $2$
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Show commands: SageMath
E = EllipticCurve("fw1")
 
E.isogeny_class()
 

Elliptic curves in class 286110fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
286110.fw2 286110fw1 \([1, -1, 1, -30230177, 63663238001]\) \(173629978755828841/1000026931200\) \(17596761690146026291200\) \([2]\) \(32440320\) \(3.1096\) \(\Gamma_0(N)\)-optimal
286110.fw1 286110fw2 \([1, -1, 1, -483012257, 4085998123889]\) \(708234550511150304361/23696640000\) \(416972897356688640000\) \([2]\) \(64880640\) \(3.4562\)  

Rank

sage: E.rank()
 

The elliptic curves in class 286110fw have rank \(2\).

Complex multiplication

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

Modular form 286110.2.a.fw

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - 2 q^{7} + q^{8} + q^{10} - q^{11} - 4 q^{13} - 2 q^{14} + q^{16} - 6 q^{19} + O(q^{20})\) 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.