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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 32340.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.bj1 | 32340bm2 | \([0, 1, 0, -542740, -154079500]\) | \(1711503051568/7425\) | \(76704136185600\) | \([2]\) | \(225792\) | \(1.8711\) | |
32340.bj2 | 32340bm1 | \([0, 1, 0, -33385, -2495452]\) | \(-6373654528/441045\) | \(-284764105589040\) | \([2]\) | \(112896\) | \(1.5245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 32340.bj do not have complex multiplication.Modular form 32340.2.a.bj
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.