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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 16080n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16080.d2 | 16080n1 | \([0, -1, 0, 3819, -15075]\) | \(1503484706816/890163675\) | \(-3646110412800\) | \([]\) | \(34560\) | \(1.0997\) | \(\Gamma_0(N)\)-optimal |
| 16080.d1 | 16080n2 | \([0, -1, 0, -48021, 4489821]\) | \(-2989967081734144/380653171875\) | \(-1559155392000000\) | \([]\) | \(103680\) | \(1.6490\) |
Rank
sage: E.rank()
The elliptic curves in class 16080n have rank \(0\).
Complex multiplication
The elliptic curves in class 16080n do not have complex multiplication.Modular form 16080.2.a.n
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.
