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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 60690z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60690.z2 | 60690z1 | \([1, 0, 1, 23547, 1662448]\) | \(59822347031/83966400\) | \(-2026744773681600\) | \([2]\) | \(331776\) | \(1.6227\) | \(\Gamma_0(N)\)-optimal |
| 60690.z1 | 60690z2 | \([1, 0, 1, -149853, 16436128]\) | \(15417797707369/4080067320\) | \(98482906461145080\) | \([2]\) | \(663552\) | \(1.9693\) |
Rank
sage: E.rank()
The elliptic curves in class 60690z have rank \(1\).
Complex multiplication
The elliptic curves in class 60690z do not have complex multiplication.Modular form 60690.2.a.z
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.
