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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 69312.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 69312.ba1 | 69312i1 | \([0, -1, 0, -26473, 1659049]\) | \(10648000/57\) | \(10983895928832\) | \([2]\) | \(138240\) | \(1.3465\) | \(\Gamma_0(N)\)-optimal |
| 69312.ba2 | 69312i2 | \([0, -1, 0, -12033, 3446721]\) | \(-125000/3249\) | \(-5008656543547392\) | \([2]\) | \(276480\) | \(1.6931\) |
Rank
sage: E.rank()
The elliptic curves in class 69312.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 69312.ba do not have complex multiplication.Modular form 69312.2.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.
