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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 330330.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
330330.a1 | 330330a1 | \([1, 1, 0, -1472088, 686544192]\) | \(199144987475642209/102211200000\) | \(181073375683200000\) | \([2]\) | \(6720000\) | \(2.2629\) | \(\Gamma_0(N)\)-optimal |
330330.a2 | 330330a2 | \([1, 1, 0, -1220408, 929214048]\) | \(-113470585236878689/145116562500000\) | \(-257082842579062500000\) | \([2]\) | \(13440000\) | \(2.6095\) |
Rank
sage: E.rank()
The elliptic curves in class 330330.a have rank \(0\).
Complex multiplication
The elliptic curves in class 330330.a do not have complex multiplication.Modular form 330330.2.a.a
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.