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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 83259e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 83259.f2 | 83259e1 | \([0, 0, 1, -174, 3487]\) | \(-950272/8019\) | \(-4916360691\) | \([]\) | \(34560\) | \(0.54234\) | \(\Gamma_0(N)\)-optimal |
| 83259.f1 | 83259e2 | \([0, 0, 1, -23664, 1401142]\) | \(-2390367404032/11979\) | \(-7344193131\) | \([]\) | \(103680\) | \(1.0916\) |
Rank
sage: E.rank()
The elliptic curves in class 83259e have rank \(2\).
Complex multiplication
The elliptic curves in class 83259e do not have complex multiplication.Modular form 83259.2.a.e
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.
