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SageMath
E = EllipticCurve("ho1")
E.isogeny_class()
Elliptic curves in class 129360ho
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.gd2 | 129360ho1 | \([0, 1, 0, 12675, 1379223]\) | \(7476617216/31444875\) | \(-947061273312000\) | \([]\) | \(497664\) | \(1.5563\) | \(\Gamma_0(N)\)-optimal |
| 129360.gd1 | 129360ho2 | \([0, 1, 0, -116685, -42189225]\) | \(-5833703071744/22107421875\) | \(-665834515500000000\) | \([]\) | \(1492992\) | \(2.1056\) |
Rank
sage: E.rank()
The elliptic curves in class 129360ho have rank \(1\).
Complex multiplication
The elliptic curves in class 129360ho do not have complex multiplication.Modular form 129360.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
