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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 274890h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.h1 | 274890h1 | \([1, 1, 0, -60148, 5117008]\) | \(204555107163961/21287481600\) | \(2504450922758400\) | \([2]\) | \(2654208\) | \(1.6899\) | \(\Gamma_0(N)\)-optimal |
274890.h2 | 274890h2 | \([1, 1, 0, 77052, 25230528]\) | \(430009859127239/2580384890160\) | \(-303579701942433840\) | \([2]\) | \(5308416\) | \(2.0364\) |
Rank
sage: E.rank()
The elliptic curves in class 274890h have rank \(0\).
Complex multiplication
The elliptic curves in class 274890h do not have complex multiplication.Modular form 274890.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.