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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 142800en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.s2 | 142800en1 | \([0, -1, 0, -673408, 556429312]\) | \(-527690404915129/1782829440000\) | \(-114101084160000000000\) | \([2]\) | \(4423680\) | \(2.5348\) | \(\Gamma_0(N)\)-optimal |
| 142800.s1 | 142800en2 | \([0, -1, 0, -15073408, 22502029312]\) | \(5918043195362419129/8515734343200\) | \(545006997964800000000\) | \([2]\) | \(8847360\) | \(2.8814\) |
Rank
sage: E.rank()
The elliptic curves in class 142800en have rank \(1\).
Complex multiplication
The elliptic curves in class 142800en do not have complex multiplication.Modular form 142800.2.a.en
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.
