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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 333960dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333960.dc2 | 333960dc1 | \([0, 1, 0, -3876880, -3065265040]\) | \(-3552342505518244/179863605135\) | \(-326286692532803312640\) | \([2]\) | \(14784000\) | \(2.6968\) | \(\Gamma_0(N)\)-optimal |
| 333960.dc1 | 333960dc2 | \([0, 1, 0, -62765160, -191413539792]\) | \(7536914291382802562/17961229575\) | \(65166159517934745600\) | \([2]\) | \(29568000\) | \(3.0434\) |
Rank
sage: E.rank()
The elliptic curves in class 333960dc have rank \(0\).
Complex multiplication
The elliptic curves in class 333960dc do not have complex multiplication.Modular form 333960.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
