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SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 129360.hn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129360.hn1 | 129360hv1 | \([0, 1, 0, -132120, -15623532]\) | \(529278808969/88704000\) | \(42745597526016000\) | \([2]\) | \(1105920\) | \(1.9122\) | \(\Gamma_0(N)\)-optimal |
129360.hn2 | 129360hv2 | \([0, 1, 0, 244200, -88027500]\) | \(3342032927351/8893500000\) | \(-4285691418624000000\) | \([2]\) | \(2211840\) | \(2.2588\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.hn have rank \(0\).
Complex multiplication
The elliptic curves in class 129360.hn do not have complex multiplication.Modular form 129360.2.a.hn
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.