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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 489762i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 489762.i2 | 489762i1 | \([1, -1, 0, -191931, -43418907]\) | \(-5999796014211/2790817792\) | \(-363710099766214656\) | \([]\) | \(10834560\) | \(2.0758\) | \(\Gamma_0(N)\)-optimal |
| 489762.i1 | 489762i2 | \([1, -1, 0, -16983771, -26935861627]\) | \(-5702623460245179/252448\) | \(-23984095274377056\) | \([]\) | \(32503680\) | \(2.6251\) |
Rank
sage: E.rank()
The elliptic curves in class 489762i have rank \(0\).
Complex multiplication
The elliptic curves in class 489762i do not have complex multiplication.Modular form 489762.2.a.i
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.
