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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 254100bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.bf2 | 254100bf1 | \([0, -1, 0, 5002342, 7335845937]\) | \(2134896896/4822335\) | \(-31269737615815833750000\) | \([]\) | \(20528640\) | \(3.0005\) | \(\Gamma_0(N)\)-optimal |
254100.bf1 | 254100bf2 | \([0, -1, 0, -192651158, 1032169243437]\) | \(-121947169848064/397065375\) | \(-2574713306432572593750000\) | \([]\) | \(61585920\) | \(3.5498\) |
Rank
sage: E.rank()
The elliptic curves in class 254100bf have rank \(0\).
Complex multiplication
The elliptic curves in class 254100bf do not have complex multiplication.Modular form 254100.2.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 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.