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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 283920.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.p1 | 283920p1 | \([0, -1, 0, -83776, -9282560]\) | \(7225996599037/20321280\) | \(182869410447360\) | \([2]\) | \(1474560\) | \(1.6088\) | \(\Gamma_0(N)\)-optimal |
| 283920.p2 | 283920p2 | \([0, -1, 0, -50496, -16763904]\) | \(-1582388942077/12602368800\) | \(-113407607822745600\) | \([2]\) | \(2949120\) | \(1.9553\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.p have rank \(1\).
Complex multiplication
The elliptic curves in class 283920.p do not have complex multiplication.Modular form 283920.2.a.p
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.
