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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 235200fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.fc2 | 235200fc1 | \([0, -1, 0, -933, -8763]\) | \(16384/3\) | \(16464000000\) | \([2]\) | \(196608\) | \(0.67894\) | \(\Gamma_0(N)\)-optimal |
235200.fc1 | 235200fc2 | \([0, -1, 0, -4433, 106737]\) | \(109744/9\) | \(790272000000\) | \([2]\) | \(393216\) | \(1.0255\) |
Rank
sage: E.rank()
The elliptic curves in class 235200fc have rank \(0\).
Complex multiplication
The elliptic curves in class 235200fc do not have complex multiplication.Modular form 235200.2.a.fc
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.