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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 98736.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.ba1 | 98736bp2 | \([0, -1, 0, -16848, 839808]\) | \(97018944875/1003833\) | \(5472672657408\) | \([2]\) | \(184320\) | \(1.2613\) | |
| 98736.ba2 | 98736bp1 | \([0, -1, 0, -1888, -9920]\) | \(136590875/70227\) | \(382861873152\) | \([2]\) | \(92160\) | \(0.91475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 98736.ba do not have complex multiplication.Modular form 98736.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
