Properties

Label 288990dw
Number of curves $2$
Conductor $288990$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dw1")
 
E.isogeny_class()
 

Elliptic curves in class 288990dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
288990.dw2 288990dw1 \([1, -1, 1, -2214608, 1274883887]\) \(-341370886042369/1817528220\) \(-6395416084566435420\) \([2]\) \(8601600\) \(2.4533\) \(\Gamma_0(N)\)-optimal
288990.dw1 288990dw2 \([1, -1, 1, -35478878, 81348634631]\) \(1403607530712116449/39475350\) \(138903641525791350\) \([2]\) \(17203200\) \(2.7999\)  

Rank

sage: E.rank()
 

The elliptic curves in class 288990dw have rank \(1\).

Complex multiplication

The elliptic curves in class 288990dw do not have complex multiplication.

Modular form 288990.2.a.dw

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.