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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 180999j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180999.j1 | 180999j1 | \([1, -1, 1, -7910753, 8564832904]\) | \(420100556152674123/62939003491\) | \(8202452809537535913\) | \([2]\) | \(7741440\) | \(2.6425\) | \(\Gamma_0(N)\)-optimal |
| 180999.j2 | 180999j2 | \([1, -1, 1, -7178138, 10214681884]\) | \(-313859434290315003/164114213839849\) | \(-21387995038532908219707\) | \([2]\) | \(15482880\) | \(2.9891\) |
Rank
sage: E.rank()
The elliptic curves in class 180999j have rank \(0\).
Complex multiplication
The elliptic curves in class 180999j do not have complex multiplication.Modular form 180999.2.a.j
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.
