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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 81120.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81120.bu1 | 81120bx4 | \([0, 1, 0, -13745, 615135]\) | \(14526784/15\) | \(296559144960\) | \([2]\) | \(147456\) | \(1.1192\) | |
| 81120.bu2 | 81120bx3 | \([0, 1, 0, -9520, -357460]\) | \(38614472/405\) | \(1000887114240\) | \([2]\) | \(147456\) | \(1.1192\) | |
| 81120.bu3 | 81120bx1 | \([0, 1, 0, -1070, 4200]\) | \(438976/225\) | \(69506049600\) | \([2, 2]\) | \(73728\) | \(0.77263\) | \(\Gamma_0(N)\)-optimal |
| 81120.bu4 | 81120bx2 | \([0, 1, 0, 4000, 36648]\) | \(2863288/1875\) | \(-4633736640000\) | \([2]\) | \(147456\) | \(1.1192\) |
Rank
sage: E.rank()
The elliptic curves in class 81120.bu have rank \(0\).
Complex multiplication
The elliptic curves in class 81120.bu do not have complex multiplication.Modular form 81120.2.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.
