Properties

Label 51600.cs
Number of curves $2$
Conductor $51600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.cs1 51600df1 \([0, 1, 0, -128, -972]\) \(-2282665/2322\) \(-237772800\) \([]\) \(17280\) \(0.30276\) \(\Gamma_0(N)\)-optimal
51600.cs2 51600df2 \([0, 1, 0, 1072, 16788]\) \(1329238535/1908168\) \(-195396403200\) \([]\) \(51840\) \(0.85207\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 51600.2.a.cs

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 4q^{13} + 6q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.