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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 485520.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.h1 | 485520h2 | \([0, -1, 0, -37454388536, -2789974521369360]\) | \(58773069105954437388714841/21507018750\) | \(2126344802559667200000\) | \([2]\) | \(530841600\) | \(4.3501\) | \(\Gamma_0(N)\)-optimal* |
485520.h2 | 485520h1 | \([0, -1, 0, -2340888536, -43593186969360]\) | \(-14348696196102335214841/274485585937500\) | \(-27137698898214240000000000\) | \([2]\) | \(265420800\) | \(4.0035\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520.h have rank \(0\).
Complex multiplication
The elliptic curves in class 485520.h do not have complex multiplication.Modular form 485520.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.