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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 84966f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.f2 | 84966f1 | \([1, 1, 0, -3768376924, 89035255022176]\) | \(42531320912955257257/1127938881456\) | \(156950757452701066497887664\) | \([]\) | \(121927680\) | \(4.1318\) | \(\Gamma_0(N)\)-optimal |
84966.f1 | 84966f2 | \([1, 1, 0, -6538480939, -58252741166339]\) | \(222165413800219579417/118033833938006016\) | \(16424205199578486928066285154304\) | \([]\) | \(365783040\) | \(4.6811\) |
Rank
sage: E.rank()
The elliptic curves in class 84966f have rank \(1\).
Complex multiplication
The elliptic curves in class 84966f do not have complex multiplication.Modular form 84966.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.