Properties

Label 154560.eh
Number of curves $4$
Conductor $154560$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154560.eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.eh1 154560bu3 \([0, 1, 0, -741921, 245724255]\) \(344577854816148242/2716875\) \(356106240000\) \([2]\) \(983040\) \(1.8075\)  
154560.eh2 154560bu2 \([0, 1, 0, -46401, 3822399]\) \(168591300897604/472410225\) \(30959876505600\) \([2, 2]\) \(491520\) \(1.4609\)  
154560.eh3 154560bu4 \([0, 1, 0, -28001, 6902559]\) \(-18524646126002/146738831715\) \(-19233352150548480\) \([2]\) \(983040\) \(1.8075\)  
154560.eh4 154560bu1 \([0, 1, 0, -4081, 5135]\) \(458891455696/264449745\) \(4332744622080\) \([2]\) \(245760\) \(1.1143\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 154560.eh have rank \(2\).

Complex multiplication

The elliptic curves in class 154560.eh do not have complex multiplication.

Modular form 154560.2.a.eh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.