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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 43120x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43120.t2 | 43120x1 | \([0, -1, 0, -231296, 30109696]\) | \(57954303169/17036800\) | \(402283567828172800\) | \([]\) | \(435456\) | \(2.0838\) | \(\Gamma_0(N)\)-optimal |
| 43120.t1 | 43120x2 | \([0, -1, 0, -17134336, 27304855040]\) | \(23560326604350529/1375000\) | \(32467359232000000\) | \([]\) | \(1306368\) | \(2.6331\) |
Rank
sage: E.rank()
The elliptic curves in class 43120x have rank \(0\).
Complex multiplication
The elliptic curves in class 43120x do not have complex multiplication.Modular form 43120.2.a.x
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.
