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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 2093.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2093.h1 | 2093f3 | \([0, 1, 1, -14829659, -21985816061]\) | \(-360675992659311050823073792/56219378022244619\) | \(-56219378022244619\) | \([]\) | \(69984\) | \(2.6183\) | |
| 2093.h2 | 2093f2 | \([0, 1, 1, -159549, -38239046]\) | \(-449167881463536812032/369990050199923699\) | \(-369990050199923699\) | \([3]\) | \(23328\) | \(2.0690\) | |
| 2093.h3 | 2093f1 | \([0, 1, 1, 16211, 856569]\) | \(471114356703100928/585612268875179\) | \(-585612268875179\) | \([3]\) | \(7776\) | \(1.5197\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2093.h have rank \(1\).
Complex multiplication
The elliptic curves in class 2093.h do not have complex multiplication.Modular form 2093.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
