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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 201810ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 201810.r3 | 201810ci1 | \([1, 1, 0, -108132, -377366724]\) | \(-157551496201/69209437500\) | \(-61423630541189437500\) | \([2]\) | \(6635520\) | \(2.4762\) | \(\Gamma_0(N)\)-optimal |
| 201810.r2 | 201810ci2 | \([1, 1, 0, -8516882, -9473952474]\) | \(76983121960756201/893750901750\) | \(793207215200194341750\) | \([2]\) | \(13271040\) | \(2.8227\) | |
| 201810.r4 | 201810ci3 | \([1, 1, 0, 972993, 10176359301]\) | \(114784170265799/50470291569600\) | \(-44792569549163267697600\) | \([2]\) | \(19906560\) | \(3.0255\) | |
| 201810.r1 | 201810ci4 | \([1, 1, 0, -64951607, 196360614621]\) | \(34144696869398652601/986300590768920\) | \(875345404879891120394520\) | \([2]\) | \(39813120\) | \(3.3720\) |
Rank
sage: E.rank()
The elliptic curves in class 201810ci have rank \(0\).
Complex multiplication
The elliptic curves in class 201810ci do not have complex multiplication.Modular form 201810.2.a.ci
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
