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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 471600en
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 471600.en2 | 471600en1 | \([0, 0, 0, -7686075, 7795638250]\) | \(1076291879750641/60150618144\) | \(2806387240126464000000\) | \([]\) | \(22579200\) | \(2.8705\) | \(\Gamma_0(N)\)-optimal |
| 471600.en1 | 471600en2 | \([0, 0, 0, -817362075, -8994338621750]\) | \(1294373635812597347281/2083292441154\) | \(97198092134481024000000\) | \([]\) | \(112896000\) | \(3.6752\) |
Rank
sage: E.rank()
The elliptic curves in class 471600en have rank \(2\).
Complex multiplication
The elliptic curves in class 471600en do not have complex multiplication.Modular form 471600.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
