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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 247962.bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.bf1 | 247962bf1 | \([1, 0, 0, -24373688, -46315015104]\) | \(66342819962001390625/4812668669952\) | \(116166122095104626688\) | \([2]\) | \(17031168\) | \(2.9013\) | \(\Gamma_0(N)\)-optimal |
247962.bf2 | 247962bf2 | \([1, 0, 0, -22801528, -52548000640]\) | \(-54315282059491182625/17983956399469632\) | \(-434088988485189805804608\) | \([2]\) | \(34062336\) | \(3.2479\) |
Rank
sage: E.rank()
The elliptic curves in class 247962.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 247962.bf do not have complex multiplication.Modular form 247962.2.a.bf
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.