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SageMath
E = EllipticCurve("hn1")
E.isogeny_class()
Elliptic curves in class 33600.hn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33600.hn1 | 33600dz1 | \([0, 1, 0, -28833, 1814463]\) | \(5177717/189\) | \(96768000000000\) | \([2]\) | \(122880\) | \(1.4532\) | \(\Gamma_0(N)\)-optimal |
33600.hn2 | 33600dz2 | \([0, 1, 0, 11167, 6494463]\) | \(300763/35721\) | \(-18289152000000000\) | \([2]\) | \(245760\) | \(1.7998\) |
Rank
sage: E.rank()
The elliptic curves in class 33600.hn have rank \(0\).
Complex multiplication
The elliptic curves in class 33600.hn do not have complex multiplication.Modular form 33600.2.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.