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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 46800.fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.fc1 | 46800fo2 | \([0, 0, 0, -507315, 138638450]\) | \(38686490446661/141927552\) | \(52974174928896000\) | \([2]\) | \(688128\) | \(2.0695\) | |
46800.fc2 | 46800fo1 | \([0, 0, 0, -46515, -62350]\) | \(29819839301/17252352\) | \(6439405879296000\) | \([2]\) | \(344064\) | \(1.7229\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.fc have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.fc do not have complex multiplication.Modular form 46800.2.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 LMFDB 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 LMFDB labels.