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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 132600bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132600.cf1 | 132600bu1 | \([0, 1, 0, -2442508, -1426112512]\) | \(402876451435348816/13746755117745\) | \(54987020470980000000\) | \([2]\) | \(4423680\) | \(2.5598\) | \(\Gamma_0(N)\)-optimal |
| 132600.cf2 | 132600bu2 | \([0, 1, 0, 837992, -4969052512]\) | \(4067455675907516/669098843633025\) | \(-10705581498128400000000\) | \([2]\) | \(8847360\) | \(2.9064\) |
Rank
sage: E.rank()
The elliptic curves in class 132600bu have rank \(0\).
Complex multiplication
The elliptic curves in class 132600bu do not have complex multiplication.Modular form 132600.2.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.
