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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 206400.fc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206400.fc1 | 206400kp2 | \([0, -1, 0, -265241633, -1662596608863]\) | \(503835593418244309249/898614000000\) | \(3680722944000000000000\) | \([2]\) | \(46448640\) | \(3.3964\) | |
206400.fc2 | 206400kp1 | \([0, -1, 0, -16409633, -26526208863]\) | \(-119305480789133569/5200091136000\) | \(-21299573293056000000000\) | \([2]\) | \(23224320\) | \(3.0499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206400.fc have rank \(1\).
Complex multiplication
The elliptic curves in class 206400.fc do not have complex multiplication.Modular form 206400.2.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.