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SageMath
E = EllipticCurve("kl1")
E.isogeny_class()
Elliptic curves in class 235200kl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.kl1 | 235200kl1 | \([0, -1, 0, -13368833, -18708734463]\) | \(4386781853/27216\) | \(1639390814208000000000\) | \([2]\) | \(14745600\) | \(2.9087\) | \(\Gamma_0(N)\)-optimal |
| 235200.kl2 | 235200kl2 | \([0, -1, 0, -5528833, -40480414463]\) | \(-310288733/11573604\) | \(-697150943741952000000000\) | \([2]\) | \(29491200\) | \(3.2553\) |
Rank
sage: E.rank()
The elliptic curves in class 235200kl have rank \(1\).
Complex multiplication
The elliptic curves in class 235200kl do not have complex multiplication.Modular form 235200.2.a.kl
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.
