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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 166410.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166410.z1 | 166410bp2 | \([1, -1, 0, -8445654, -9442472940]\) | \(14457238157881/4437600\) | \(20449675205690709600\) | \([2]\) | \(7096320\) | \(2.6822\) | |
| 166410.z2 | 166410bp1 | \([1, -1, 0, -457974, -187946892]\) | \(-2305199161/1981440\) | \(-9131017766261898240\) | \([2]\) | \(3548160\) | \(2.3357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 166410.z have rank \(0\).
Complex multiplication
The elliptic curves in class 166410.z do not have complex multiplication.Modular form 166410.2.a.z
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 LMFDB 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 LMFDB labels.
