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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 208080.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 208080.dv1 | 208080eh4 | \([0, 0, 0, -278307, -56509326]\) | \(132304644/5\) | \(90092993541120\) | \([2]\) | \(1310720\) | \(1.7637\) | |
| 208080.dv2 | 208080eh2 | \([0, 0, 0, -18207, -795906]\) | \(148176/25\) | \(112616241926400\) | \([2, 2]\) | \(655360\) | \(1.4171\) | |
| 208080.dv3 | 208080eh1 | \([0, 0, 0, -5202, 132651]\) | \(55296/5\) | \(1407703024080\) | \([2]\) | \(327680\) | \(1.0706\) | \(\Gamma_0(N)\)-optimal |
| 208080.dv4 | 208080eh3 | \([0, 0, 0, 33813, -4510134]\) | \(237276/625\) | \(-11261624192640000\) | \([2]\) | \(1310720\) | \(1.7637\) |
Rank
sage: E.rank()
The elliptic curves in class 208080.dv have rank \(1\).
Complex multiplication
The elliptic curves in class 208080.dv do not have complex multiplication.Modular form 208080.2.a.dv
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
