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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 257600.fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.fb1 | 257600fb1 | \([0, -1, 0, -254633, 49356137]\) | \(28529194119616/123265625\) | \(7889000000000000\) | \([2]\) | \(2211840\) | \(1.9037\) | \(\Gamma_0(N)\)-optimal |
257600.fb2 | 257600fb2 | \([0, -1, 0, -129633, 97731137]\) | \(-470547874952/7779540125\) | \(-3983124544000000000\) | \([2]\) | \(4423680\) | \(2.2503\) |
Rank
sage: E.rank()
The elliptic curves in class 257600.fb have rank \(1\).
Complex multiplication
The elliptic curves in class 257600.fb do not have complex multiplication.Modular form 257600.2.a.fb
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.