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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 290145f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290145.f1 | 290145f1 | \([1, 1, 1, -314131, 67630928]\) | \(5763259856089/450225\) | \(267804329697225\) | \([2]\) | \(1451520\) | \(1.8157\) | \(\Gamma_0(N)\)-optimal |
290145.f2 | 290145f2 | \([1, 1, 1, -293106, 77100588]\) | \(-4681768588489/1621620405\) | \(-964577634703465005\) | \([2]\) | \(2903040\) | \(2.1623\) |
Rank
sage: E.rank()
The elliptic curves in class 290145f have rank \(1\).
Complex multiplication
The elliptic curves in class 290145f do not have complex multiplication.Modular form 290145.2.a.f
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.