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Properties

Label 164730.dc
Number of curves $2$
Conductor $164730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dc1")
 
E.isogeny_class()
 

Elliptic curves in class 164730.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.dc1 164730k2 \([1, 0, 0, -8676, -306870]\) \(2992209121/54150\) \(1307049361350\) \([2]\) \(399360\) \(1.1202\)  
164730.dc2 164730k1 \([1, 0, 0, -6, -13824]\) \(-1/3420\) \(-82550485980\) \([2]\) \(199680\) \(0.77361\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 164730.dc have rank \(0\).

Complex multiplication

The elliptic curves in class 164730.dc do not have complex multiplication.

Modular form 164730.2.a.dc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.