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SageMath
E = EllipticCurve("ki1")
E.isogeny_class()
Elliptic curves in class 187200ki
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.or2 | 187200ki1 | \([0, 0, 0, -4651500, 62350000]\) | \(29819839301/17252352\) | \(6439405879296000000000\) | \([2]\) | \(13762560\) | \(2.8742\) | \(\Gamma_0(N)\)-optimal |
| 187200.or1 | 187200ki2 | \([0, 0, 0, -50731500, -138638450000]\) | \(38686490446661/141927552\) | \(52974174928896000000000\) | \([2]\) | \(27525120\) | \(3.2208\) |
Rank
sage: E.rank()
The elliptic curves in class 187200ki have rank \(0\).
Complex multiplication
The elliptic curves in class 187200ki do not have complex multiplication.Modular form 187200.2.a.ki
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.
