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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 89280do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.fb1 | 89280do1 | \([0, 0, 0, -45612, -4402736]\) | \(-1482713947827/325058560\) | \(-2300728081121280\) | \([]\) | \(387072\) | \(1.6684\) | \(\Gamma_0(N)\)-optimal |
| 89280.fb2 | 89280do2 | \([0, 0, 0, 323028, 26448336]\) | \(722458663317/476656000\) | \(-2459440263462912000\) | \([]\) | \(1161216\) | \(2.2177\) |
Rank
sage: E.rank()
The elliptic curves in class 89280do have rank \(1\).
Complex multiplication
The elliptic curves in class 89280do do not have complex multiplication.Modular form 89280.2.a.do
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.
