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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 372810.bh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
372810.bh1 | 372810bh1 | \([1, 0, 1, -44658454, -114583099048]\) | \(408076159454905367161/1190206406250000\) | \(28728689255101406250000\) | \([2]\) | \(54743040\) | \(3.1798\) | \(\Gamma_0(N)\)-optimal |
372810.bh2 | 372810bh2 | \([1, 0, 1, -26595954, -208117949048]\) | \(-86193969101536367161/725294740213012500\) | \(-17506851837228663916612500\) | \([2]\) | \(109486080\) | \(3.5264\) |
Rank
sage: E.rank()
The elliptic curves in class 372810.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 372810.bh do not have complex multiplication.Modular form 372810.2.a.bh
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.