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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 3648.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3648.ba1 | 3648o1 | \([0, 1, 0, -73, -265]\) | \(10648000/57\) | \(233472\) | \([2]\) | \(384\) | \(-0.12571\) | \(\Gamma_0(N)\)-optimal |
3648.ba2 | 3648o2 | \([0, 1, 0, -33, -513]\) | \(-125000/3249\) | \(-106463232\) | \([2]\) | \(768\) | \(0.22087\) |
Rank
sage: E.rank()
The elliptic curves in class 3648.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 3648.ba do not have complex multiplication.Modular form 3648.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.