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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 94815.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94815.h1 | 94815g2 | \([1, -1, 1, -61250132, 184520530856]\) | \(8000051600110940079507/144453125\) | \(458858673984375\) | \([2]\) | \(5160960\) | \(2.8042\) | |
94815.h2 | 94815g1 | \([1, -1, 1, -3828257, 2883655856]\) | \(1953326569433829507/262451171875\) | \(833682183837890625\) | \([2]\) | \(2580480\) | \(2.4576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94815.h have rank \(1\).
Complex multiplication
The elliptic curves in class 94815.h do not have complex multiplication.Modular form 94815.2.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.