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SageMath
E = EllipticCurve("cs1")
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)
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.