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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 98736.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.h1 | 98736cq2 | \([0, -1, 0, -2374544, -812506176]\) | \(204055591784617/78708537864\) | \(571133853888043843584\) | \([2]\) | \(3870720\) | \(2.6819\) | |
| 98736.h2 | 98736cq1 | \([0, -1, 0, -1058064, 410240448]\) | \(18052771191337/444958272\) | \(3228756874455416832\) | \([2]\) | \(1935360\) | \(2.3353\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.h have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.h do not have complex multiplication.Modular form 98736.2.a.h
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.
