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SageMath
E = EllipticCurve("do1")
E.isogeny_class()
Elliptic curves in class 164934do
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164934.bd2 | 164934do1 | \([1, -1, 0, -181598076, -905321934000]\) | \(7722211175253055152433/340131399900069888\) | \(29171750799728781922664448\) | \([2]\) | \(46725120\) | \(3.6493\) | \(\Gamma_0(N)\)-optimal |
| 164934.bd1 | 164934do2 | \([1, -1, 0, -488675196, 2964034024272]\) | \(150476552140919246594353/42832838728685592576\) | \(3673606429177934703829917696\) | \([2]\) | \(93450240\) | \(3.9959\) |
Rank
sage: E.rank()
The elliptic curves in class 164934do have rank \(0\).
Complex multiplication
The elliptic curves in class 164934do do not have complex multiplication.Modular form 164934.2.a.do
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.
