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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 16830bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.cg1 | 16830bo1 | \([1, -1, 1, -857, 12089]\) | \(-2575296504243/765952000\) | \(-20680704000\) | \([3]\) | \(14400\) | \(0.69368\) | \(\Gamma_0(N)\)-optimal |
16830.cg2 | 16830bo2 | \([1, -1, 1, 6343, -100871]\) | \(1434104310933/1046272480\) | \(-20593781223840\) | \([]\) | \(43200\) | \(1.2430\) |
Rank
sage: E.rank()
The elliptic curves in class 16830bo have rank \(1\).
Complex multiplication
The elliptic curves in class 16830bo do not have complex multiplication.Modular form 16830.2.a.bo
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.