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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 152592bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152592.q2 | 152592bu1 | \([0, -1, 0, -1864, -29456]\) | \(35611289/1188\) | \(23906893824\) | \([2]\) | \(147456\) | \(0.76425\) | \(\Gamma_0(N)\)-optimal |
| 152592.q1 | 152592bu2 | \([0, -1, 0, -4584, 79344]\) | \(529475129/176418\) | \(3550173732864\) | \([2]\) | \(294912\) | \(1.1108\) |
Rank
sage: E.rank()
The elliptic curves in class 152592bu have rank \(1\).
Complex multiplication
The elliptic curves in class 152592bu do not have complex multiplication.Modular form 152592.2.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.
