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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 83790t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83790.cp2 | 83790t1 | \([1, -1, 0, -27204, -605872]\) | \(961504803/486400\) | \(1126349313868800\) | \([2]\) | \(552960\) | \(1.5807\) | \(\Gamma_0(N)\)-optimal |
| 83790.cp1 | 83790t2 | \([1, -1, 0, -238884, 44566640]\) | \(651038076963/7220000\) | \(16719247627740000\) | \([2]\) | \(1105920\) | \(1.9273\) |
Rank
sage: E.rank()
The elliptic curves in class 83790t have rank \(0\).
Complex multiplication
The elliptic curves in class 83790t do not have complex multiplication.Modular form 83790.2.a.t
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.
