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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 4410.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4410.h1 | 4410i1 | \([1, -1, 0, -1185, 16001]\) | \(-5154200289/20\) | \(-714420\) | \([]\) | \(1680\) | \(0.33648\) | \(\Gamma_0(N)\)-optimal |
4410.h2 | 4410i2 | \([1, -1, 0, 8265, -151075]\) | \(1747829720511/1280000000\) | \(-45722880000000\) | \([]\) | \(11760\) | \(1.3094\) |
Rank
sage: E.rank()
The elliptic curves in class 4410.h have rank \(1\).
Complex multiplication
The elliptic curves in class 4410.h do not have complex multiplication.Modular form 4410.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.