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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 72450.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.h1 | 72450d1 | \([1, -1, 0, -3792, 77616]\) | \(14295828483/2254000\) | \(950906250000\) | \([2]\) | \(110592\) | \(1.0212\) | \(\Gamma_0(N)\)-optimal |
| 72450.h2 | 72450d2 | \([1, -1, 0, 6708, 424116]\) | \(79119341757/231437500\) | \(-97637695312500\) | \([2]\) | \(221184\) | \(1.3678\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.h have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.h do not have complex multiplication.Modular form 72450.2.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.
