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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 15246h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15246.a2 | 15246h1 | \([1, -1, 0, -369, 2569]\) | \(5735339/588\) | \(570535812\) | \([2]\) | \(12288\) | \(0.41576\) | \(\Gamma_0(N)\)-optimal |
15246.a1 | 15246h2 | \([1, -1, 0, -1359, -16241]\) | \(286191179/43218\) | \(41934382182\) | \([2]\) | \(24576\) | \(0.76233\) |
Rank
sage: E.rank()
The elliptic curves in class 15246h have rank \(2\).
Complex multiplication
The elliptic curves in class 15246h do not have complex multiplication.Modular form 15246.2.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.