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SageMath
E = EllipticCurve("oy1")
E.isogeny_class()
Elliptic curves in class 100800oy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.bv2 | 100800oy1 | \([0, 0, 0, 1500, -65000]\) | \(1280/7\) | \(-2041200000000\) | \([]\) | \(138240\) | \(1.0441\) | \(\Gamma_0(N)\)-optimal |
| 100800.bv1 | 100800oy2 | \([0, 0, 0, -88500, -10145000]\) | \(-262885120/343\) | \(-100018800000000\) | \([]\) | \(414720\) | \(1.5934\) |
Rank
sage: E.rank()
The elliptic curves in class 100800oy have rank \(0\).
Complex multiplication
The elliptic curves in class 100800oy do not have complex multiplication.Modular form 100800.2.a.oy
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.
