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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 238260.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238260.p1 | 238260p2 | \([0, 1, 0, -1601856756, -24676533287100]\) | \(37742718081636665212624/893153814500475\) | \(10756917266351467851129600\) | \([2]\) | \(99532800\) | \(3.9147\) | |
| 238260.p2 | 238260p1 | \([0, 1, 0, -103816861, -355555983796]\) | \(164393941520365256704/22596042787767405\) | \(17008811841027417460940880\) | \([2]\) | \(49766400\) | \(3.5681\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 238260.p have rank \(0\).
Complex multiplication
The elliptic curves in class 238260.p do not have complex multiplication.Modular form 238260.2.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.
