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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 364560du
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 364560.du2 | 364560du1 | \([0, 1, 0, -10699656, 13486893300]\) | \(-281115640967896441/468084326400\) | \(-225565298346531225600\) | \([2]\) | \(14376960\) | \(2.8013\) | \(\Gamma_0(N)\)-optimal |
| 364560.du1 | 364560du2 | \([0, 1, 0, -171262856, 862609320180]\) | \(1152829477932246539641/3188367360\) | \(1536443316374077440\) | \([2]\) | \(28753920\) | \(3.1478\) |
Rank
sage: E.rank()
The elliptic curves in class 364560du have rank \(1\).
Complex multiplication
The elliptic curves in class 364560du do not have complex multiplication.Modular form 364560.2.a.du
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
