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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 100800dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.df3 | 100800dc1 | \([0, 0, 0, -36300, -2522000]\) | \(1771561/105\) | \(313528320000000\) | \([2]\) | \(393216\) | \(1.5346\) | \(\Gamma_0(N)\)-optimal |
| 100800.df2 | 100800dc2 | \([0, 0, 0, -108300, 10582000]\) | \(47045881/11025\) | \(32920473600000000\) | \([2, 2]\) | \(786432\) | \(1.8812\) | |
| 100800.df4 | 100800dc3 | \([0, 0, 0, 251700, 66022000]\) | \(590589719/972405\) | \(-2903585771520000000\) | \([2]\) | \(1572864\) | \(2.2278\) | |
| 100800.df1 | 100800dc4 | \([0, 0, 0, -1620300, 793798000]\) | \(157551496201/13125\) | \(39191040000000000\) | \([2]\) | \(1572864\) | \(2.2278\) |
Rank
sage: E.rank()
The elliptic curves in class 100800dc have rank \(0\).
Complex multiplication
The elliptic curves in class 100800dc do not have complex multiplication.Modular form 100800.2.a.dc
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
