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SageMath
E = EllipticCurve("bqh1")
E.isogeny_class()
Elliptic curves in class 705600.bqh
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
705600.bqh1 | \([0, 0, 0, -13068300, 13008618000]\) | \(55306341/15625\) | \(69731032896000000000000\) | \([2]\) | \(66060288\) | \(3.0901\) |
705600.bqh2 | \([0, 0, 0, -4836300, -3932838000]\) | \(2803221/125\) | \(557848263168000000000\) | \([2]\) | \(33030144\) | \(2.7435\) |
Rank
sage: E.rank()
The elliptic curves in class 705600.bqh have rank \(1\).
Complex multiplication
The elliptic curves in class 705600.bqh do not have complex multiplication.Modular form 705600.2.a.bqh
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.