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SageMath
E = EllipticCurve("ho1")
E.isogeny_class()
Elliptic curves in class 106722ho
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106722.dz2 | 106722ho1 | \([1, -1, 1, -21612317, -60393128155]\) | \(-7347774183121/6119866368\) | \(-929851976284739097182208\) | \([2]\) | \(30965760\) | \(3.2970\) | \(\Gamma_0(N)\)-optimal |
| 106722.dz1 | 106722ho2 | \([1, -1, 1, -397273757, -3046901576155]\) | \(45637459887836881/13417633152\) | \(2038674041754964199574912\) | \([2]\) | \(61931520\) | \(3.6435\) |
Rank
sage: E.rank()
The elliptic curves in class 106722ho have rank \(1\).
Complex multiplication
The elliptic curves in class 106722ho do not have complex multiplication.Modular form 106722.2.a.ho
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.
