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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 19890.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19890.h1 | 19890a2 | \([1, -1, 0, -40725, -3152779]\) | \(276661817356633227/36134525440\) | \(975632186880\) | \([2]\) | \(50688\) | \(1.3209\) | |
| 19890.h2 | 19890a1 | \([1, -1, 0, -2325, -57739]\) | \(-51491303564427/24621875200\) | \(-664790630400\) | \([2]\) | \(25344\) | \(0.97432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19890.h have rank \(0\).
Complex multiplication
The elliptic curves in class 19890.h do not have complex multiplication.Modular form 19890.2.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.
