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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 272322h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272322.h4 | 272322h1 | \([1, -1, 0, 4728, -20566]\) | \(3375/2\) | \(-6925651983378\) | \([]\) | \(403920\) | \(1.1532\) | \(\Gamma_0(N)\)-optimal |
| 272322.h3 | 272322h2 | \([1, -1, 0, -70917, -7600195]\) | \(-140625/8\) | \(-2243911242614472\) | \([]\) | \(1211760\) | \(1.7025\) | |
| 272322.h1 | 272322h3 | \([1, -1, 0, -1810752, 938310272]\) | \(-189613868625/128\) | \(-443241726936192\) | \([]\) | \(2827440\) | \(2.1262\) | |
| 272322.h2 | 272322h4 | \([1, -1, 0, -1432527, 1340938349]\) | \(-1159088625/2097152\) | \(-588227868783928147968\) | \([]\) | \(8482320\) | \(2.6755\) |
Rank
sage: E.rank()
The elliptic curves in class 272322h have rank \(0\).
Complex multiplication
The elliptic curves in class 272322h do not have complex multiplication.Modular form 272322.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
