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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 104742.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104742.h1 | 104742ba2 | \([1, -1, 0, -111855033, -455298047955]\) | \(117872434296791/2811072\) | \(3691050794671442266944\) | \([2]\) | \(15261696\) | \(3.2495\) | |
| 104742.h2 | 104742ba1 | \([1, -1, 0, -6732153, -7663800339]\) | \(-25698491351/4460544\) | \(-5856873988238982770688\) | \([2]\) | \(7630848\) | \(2.9029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 104742.h have rank \(0\).
Complex multiplication
The elliptic curves in class 104742.h do not have complex multiplication.Modular form 104742.2.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.
