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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 162450dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.c2 | 162450dc1 | \([1, -1, 0, -78546267, -258877792859]\) | \(14580432307/559872\) | \(2057873673544434468000000\) | \([2]\) | \(43581440\) | \(3.4331\) | \(\Gamma_0(N)\)-optimal |
| 162450.c1 | 162450dc2 | \([1, -1, 0, -202008267, 755115613141]\) | \(248028267187/76527504\) | \(281285607752604886344750000\) | \([2]\) | \(87162880\) | \(3.7797\) |
Rank
sage: E.rank()
The elliptic curves in class 162450dc have rank \(0\).
Complex multiplication
The elliptic curves in class 162450dc do not have complex multiplication.Modular form 162450.2.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.
