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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 48400dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48400.cz2 | 48400dc1 | \([0, -1, 0, -3208, -35088]\) | \(18865/8\) | \(1548800000000\) | \([]\) | \(69120\) | \(1.0358\) | \(\Gamma_0(N)\)-optimal |
| 48400.cz1 | 48400dc2 | \([0, -1, 0, -223208, -40515088]\) | \(6352571665/2\) | \(387200000000\) | \([]\) | \(207360\) | \(1.5851\) |
Rank
sage: E.rank()
The elliptic curves in class 48400dc have rank \(0\).
Complex multiplication
The elliptic curves in class 48400dc do not have complex multiplication.Modular form 48400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
