Properties

Label 51600.ct
Number of curves $4$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.ct1 51600u4 \([0, 1, 0, -6192008, -5932620012]\) \(820480625548035842/5805\) \(185760000000\) \([2]\) \(811008\) \(2.2167\)  
51600.ct2 51600u3 \([0, 1, 0, -414008, -79128012]\) \(245245463376482/57692266875\) \(1846152540000000000\) \([2]\) \(811008\) \(2.2167\)  
51600.ct3 51600u2 \([0, 1, 0, -387008, -92790012]\) \(400649568576484/33698025\) \(539168400000000\) \([2, 2]\) \(405504\) \(1.8701\)  
51600.ct4 51600u1 \([0, 1, 0, -22508, -1665012]\) \(-315278049616/114259815\) \(-457039260000000\) \([2]\) \(202752\) \(1.5235\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 51600.ct have rank \(0\).

Complex multiplication

The elliptic curves in class 51600.ct do not have complex multiplication.

Modular form 51600.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.