Properties

Label 164730.p
Number of curves $4$
Conductor $164730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 164730.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.p1 164730cl4 \([1, 1, 0, -356465177, -2590581283611]\) \(207530301091125281552569/805586668007040\) \(19444903784500020485760\) \([2]\) \(45875200\) \(3.4900\)  
164730.p2 164730cl3 \([1, 1, 0, -67557657, 164992969701]\) \(1412712966892699019449/330160465517040000\) \(7969271017489673675760000\) \([2]\) \(45875200\) \(3.4900\)  
164730.p3 164730cl2 \([1, 1, 0, -22612377, -39211415451]\) \(52974743974734147769/3152005008998400\) \(76081738393044500889600\) \([2, 2]\) \(22937600\) \(3.1434\)  
164730.p4 164730cl1 \([1, 1, 0, 1062503, -2529556379]\) \(5495662324535111/117739817533440\) \(-2841952969760817807360\) \([2]\) \(11468800\) \(2.7969\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 164730.2.a.p

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.