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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 222768.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 222768.h1 | 222768co1 | \([0, 0, 0, -748947, -249441390]\) | \(420100556152674123/62939003491\) | \(6960550274076672\) | \([2]\) | \(2949120\) | \(2.0532\) | \(\Gamma_0(N)\)-optimal |
| 222768.h2 | 222768co2 | \([0, 0, 0, -679587, -297507870]\) | \(-313859434290315003/164114213839849\) | \(-18149719136976580608\) | \([2]\) | \(5898240\) | \(2.3998\) |
Rank
sage: E.rank()
The elliptic curves in class 222768.h have rank \(1\).
Complex multiplication
The elliptic curves in class 222768.h do not have complex multiplication.Modular form 222768.2.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.
