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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 381150p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.p2 | 381150p1 | \([1, -1, 0, -16412446617, 889626289130541]\) | \(-1787281834251393315/215504279044096\) | \(-58953086601670241235763200000000\) | \([]\) | \(1277337600\) | \(4.8314\) | \(\Gamma_0(N)\)-optimal |
| 381150.p1 | 381150p2 | \([1, -1, 0, -1365727006617, 614319359347690541]\) | \(-1412658626195854329435/1927561216\) | \(-384402636879737942188800000000\) | \([]\) | \(3832012800\) | \(5.3807\) |
Rank
sage: E.rank()
The elliptic curves in class 381150p have rank \(1\).
Complex multiplication
The elliptic curves in class 381150p do not have complex multiplication.Modular form 381150.2.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 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.
