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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 84966u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.bb2 | 84966u1 | \([1, 1, 0, -47220149, -140442814035]\) | \(-4100379159705193/626805817344\) | \(-1779978623955903703793664\) | \([2]\) | \(18579456\) | \(3.3824\) | \(\Gamma_0(N)\)-optimal |
84966.bb1 | 84966u2 | \([1, 1, 0, -781326389, -8406332255187]\) | \(18575453384550358633/352517816448\) | \(1001066295938163049461888\) | \([2]\) | \(37158912\) | \(3.7290\) |
Rank
sage: E.rank()
The elliptic curves in class 84966u have rank \(0\).
Complex multiplication
The elliptic curves in class 84966u do not have complex multiplication.Modular form 84966.2.a.u
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.