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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 229320.ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 229320.ca1 | 229320bu1 | \([0, 0, 0, -1585983, 767896738]\) | \(20093868785104/26374985\) | \(579092519650095360\) | \([2]\) | \(4423680\) | \(2.3150\) | \(\Gamma_0(N)\)-optimal |
| 229320.ca2 | 229320bu2 | \([0, 0, 0, -1153803, 1195668502]\) | \(-1934207124196/5912841025\) | \(-519292353335207961600\) | \([2]\) | \(8847360\) | \(2.6616\) |
Rank
sage: E.rank()
The elliptic curves in class 229320.ca have rank \(1\).
Complex multiplication
The elliptic curves in class 229320.ca do not have complex multiplication.Modular form 229320.2.a.ca
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 LMFDB 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 LMFDB labels.
