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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 215985.bu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
215985.bu1 | 215985bp4 | \([1, 0, 1, -204009, -35482163]\) | \(530044731605089/26309115\) | \(46608202078515\) | \([2]\) | \(1474560\) | \(1.6941\) | |
215985.bu2 | 215985bp3 | \([1, 0, 1, -64859, 5904677]\) | \(17032120495489/1339001685\) | \(2372123164080285\) | \([2]\) | \(1474560\) | \(1.6941\) | |
215985.bu3 | 215985bp2 | \([1, 0, 1, -13434, -492593]\) | \(151334226289/28676025\) | \(50801327525025\) | \([2, 2]\) | \(737280\) | \(1.3475\) | |
215985.bu4 | 215985bp1 | \([1, 0, 1, 1691, -44893]\) | \(302111711/669375\) | \(-1185838644375\) | \([2]\) | \(368640\) | \(1.0009\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 215985.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 215985.bu do not have complex multiplication.Modular form 215985.2.a.bu
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.