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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 90972k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 90972.j2 | 90972k1 | \([0, 0, 0, -745104, 573432977]\) | \(-83369132032/210622923\) | \(-115577887489595021232\) | \([2]\) | \(2764800\) | \(2.5375\) | \(\Gamma_0(N)\)-optimal |
| 90972.j1 | 90972k2 | \([0, 0, 0, -15869199, 24309187670]\) | \(50338425969232/54974619\) | \(482671134865247521536\) | \([2]\) | \(5529600\) | \(2.8841\) |
Rank
sage: E.rank()
The elliptic curves in class 90972k have rank \(1\).
Complex multiplication
The elliptic curves in class 90972k do not have complex multiplication.Modular form 90972.2.a.k
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.
