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SageMath
E = EllipticCurve("pj1")
E.isogeny_class()
Elliptic curves in class 141120.pj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.pj1 | 141120ou1 | \([0, 0, 0, -16069452, -24740600976]\) | \(551105805571803/1376829440\) | \(1146494748783311585280\) | \([2]\) | \(10321920\) | \(2.9183\) | \(\Gamma_0(N)\)-optimal |
| 141120.pj2 | 141120ou2 | \([0, 0, 0, -10048332, -43504819344]\) | \(-134745327251163/903920796800\) | \(-752700673546918664601600\) | \([2]\) | \(20643840\) | \(3.2649\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.pj have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.pj do not have complex multiplication.Modular form 141120.2.a.pj
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.
