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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 257600.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.ba1 | 257600ba2 | \([0, 1, 0, -10113, -906017]\) | \(-17455277065/43606528\) | \(-285779741900800\) | \([]\) | \(995328\) | \(1.4617\) | |
257600.ba2 | 257600ba1 | \([0, 1, 0, 1087, 28063]\) | \(21653735/63112\) | \(-413610803200\) | \([]\) | \(331776\) | \(0.91244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 257600.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 257600.ba do not have complex multiplication.Modular form 257600.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.