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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 89280bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89280.f1 | 89280bu1 | \([0, 0, 0, -3648, -84832]\) | \(-449511424/155\) | \(-1851310080\) | \([]\) | \(69120\) | \(0.74934\) | \(\Gamma_0(N)\)-optimal |
| 89280.f2 | 89280bu2 | \([0, 0, 0, 2112, -318688]\) | \(87228416/3723875\) | \(-44477724672000\) | \([]\) | \(207360\) | \(1.2986\) |
Rank
sage: E.rank()
The elliptic curves in class 89280bu have rank \(1\).
Complex multiplication
The elliptic curves in class 89280bu do not have complex multiplication.Modular form 89280.2.a.bu
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.
