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SageMath
E = EllipticCurve("hu1")
E.isogeny_class()
Elliptic curves in class 145600hu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145600.gd1 | 145600hu1 | \([0, -1, 0, -47633, 3717137]\) | \(46689225424/3901625\) | \(998816000000000\) | \([2]\) | \(884736\) | \(1.6201\) | \(\Gamma_0(N)\)-optimal |
145600.gd2 | 145600hu2 | \([0, -1, 0, 50367, 16947137]\) | \(13799183324/129390625\) | \(-132496000000000000\) | \([2]\) | \(1769472\) | \(1.9667\) |
Rank
sage: E.rank()
The elliptic curves in class 145600hu have rank \(1\).
Complex multiplication
The elliptic curves in class 145600hu do not have complex multiplication.Modular form 145600.2.a.hu
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.