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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 38025ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38025.bh2 | 38025ba1 | \([0, 0, 1, -5070, -129074]\) | \(163840/13\) | \(1143591722325\) | \([]\) | \(60480\) | \(1.0574\) | \(\Gamma_0(N)\)-optimal |
| 38025.bh1 | 38025ba2 | \([0, 0, 1, -81120, 8867641]\) | \(671088640/2197\) | \(193267001072925\) | \([]\) | \(181440\) | \(1.6067\) |
Rank
sage: E.rank()
The elliptic curves in class 38025ba have rank \(0\).
Complex multiplication
The elliptic curves in class 38025ba do not have complex multiplication.Modular form 38025.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
