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Properties

Label 5610.w
Number of curves $2$
Conductor $5610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.w1 5610z1 \([1, 1, 1, -1024276, -399370027]\) \(118843307222596927933249/19794099600000000\) \(19794099600000000\) \([2]\) \(134400\) \(2.1348\) \(\Gamma_0(N)\)-optimal
5610.w2 5610z2 \([1, 1, 1, -924276, -480330027]\) \(-87323024620536113533249/48975797371840020000\) \(-48975797371840020000\) \([2]\) \(268800\) \(2.4814\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.w have rank \(1\).

Complex multiplication

The elliptic curves in class 5610.w do not have complex multiplication.

Modular form 5610.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} + q^{8} + q^{9} - q^{10} + q^{11} - q^{12} + 4 q^{13} - 4 q^{14} + q^{15} + q^{16} - q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.