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Properties

Label 160113.f
Number of curves $2$
Conductor $160113$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 160113.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160113.f1 160113g2 \([0, -1, 1, -12332446, -16665400125]\) \(-9358714467168256/22284891\) \(-493930371844401939\) \([]\) \(8985600\) \(2.6366\)  
160113.f2 160113g1 \([0, -1, 1, 55244, -5726745]\) \(841232384/1121931\) \(-24866883845820099\) \([]\) \(1797120\) \(1.8318\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 160113.f have rank \(0\).

Complex multiplication

The elliptic curves in class 160113.f do not have complex multiplication.

Modular form 160113.2.a.f

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.