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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 37485.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37485.bj1 | 37485bs4 | \([1, -1, 0, -447624, 89064765]\) | \(115650783909361/27072079335\) | \(2321867231967209535\) | \([2]\) | \(589824\) | \(2.2359\) | |
37485.bj2 | 37485bs2 | \([1, -1, 0, -149949, -21134520]\) | \(4347507044161/258084225\) | \(22134882869541225\) | \([2, 2]\) | \(294912\) | \(1.8893\) | |
37485.bj3 | 37485bs1 | \([1, -1, 0, -147744, -21821157]\) | \(4158523459441/16065\) | \(1377832733865\) | \([2]\) | \(147456\) | \(1.5428\) | \(\Gamma_0(N)\)-optimal |
37485.bj4 | 37485bs3 | \([1, -1, 0, 112446, -87415497]\) | \(1833318007919/39525924375\) | \(-3389985212583099375\) | \([2]\) | \(589824\) | \(2.2359\) |
Rank
sage: E.rank()
The elliptic curves in class 37485.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 37485.bj do not have complex multiplication.Modular form 37485.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.