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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 34320.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 34320.bu1 | 34320bt4 | \([0, 1, 0, -97696, -11785996]\) | \(25176685646263969/57915000\) | \(237219840000\) | \([2]\) | \(110592\) | \(1.4262\) | |
| 34320.bu2 | 34320bt2 | \([0, 1, 0, -6176, -181260]\) | \(6361447449889/294465600\) | \(1206131097600\) | \([2, 2]\) | \(55296\) | \(1.0796\) | |
| 34320.bu3 | 34320bt1 | \([0, 1, 0, -1056, 9204]\) | \(31824875809/8785920\) | \(35987128320\) | \([2]\) | \(27648\) | \(0.73301\) | \(\Gamma_0(N)\)-optimal |
| 34320.bu4 | 34320bt3 | \([0, 1, 0, 3424, -684300]\) | \(1083523132511/50179392120\) | \(-205534790123520\) | \([2]\) | \(110592\) | \(1.4262\) |
Rank
sage: E.rank()
The elliptic curves in class 34320.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 34320.bu do not have complex multiplication.Modular form 34320.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
