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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 33930.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33930.h1 | 33930i1 | \([1, -1, 0, -17145, 847341]\) | \(764579942079121/21285239040\) | \(15516939260160\) | \([2]\) | \(110592\) | \(1.3104\) | \(\Gamma_0(N)\)-optimal |
| 33930.h2 | 33930i2 | \([1, -1, 0, 3735, 2764125]\) | \(7903193128559/4535269736400\) | \(-3306211637835600\) | \([2]\) | \(221184\) | \(1.6569\) |
Rank
sage: E.rank()
The elliptic curves in class 33930.h have rank \(1\).
Complex multiplication
The elliptic curves in class 33930.h do not have complex multiplication.Modular form 33930.2.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.
