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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 5040ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5040.bo2 | 5040ba1 | \([0, 0, 0, -12, -9]\) | \(442368/175\) | \(75600\) | \([2]\) | \(384\) | \(-0.36550\) | \(\Gamma_0(N)\)-optimal |
| 5040.bo1 | 5040ba2 | \([0, 0, 0, -87, 306]\) | \(10536048/245\) | \(1693440\) | \([2]\) | \(768\) | \(-0.018927\) |
Rank
sage: E.rank()
The elliptic curves in class 5040ba have rank \(0\).
Complex multiplication
The elliptic curves in class 5040ba do not have complex multiplication.Modular form 5040.2.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 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.
