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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 29040bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.j1 | 29040bu1 | \([0, -1, 0, -22440216, 39932106480]\) | \(129392980254539/3583180800\) | \(34606911052986502348800\) | \([2]\) | \(2838528\) | \(3.1043\) | \(\Gamma_0(N)\)-optimal |
| 29040.j2 | 29040bu2 | \([0, -1, 0, 4818664, 130736887536]\) | \(1281177907381/765275040000\) | \(-7391143991492332093440000\) | \([2]\) | \(5677056\) | \(3.4509\) |
Rank
sage: E.rank()
The elliptic curves in class 29040bu have rank \(0\).
Complex multiplication
The elliptic curves in class 29040bu do not have complex multiplication.Modular form 29040.2.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 Cremona 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 Cremona labels.
