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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 18240p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.bj2 | 18240p1 | \([0, -1, 0, -93185, -10968063]\) | \(-341370886042369/1817528220\) | \(-476454117703680\) | \([2]\) | \(107520\) | \(1.6612\) | \(\Gamma_0(N)\)-optimal |
| 18240.bj1 | 18240p2 | \([0, -1, 0, -1492865, -701570175]\) | \(1403607530712116449/39475350\) | \(10348226150400\) | \([2]\) | \(215040\) | \(2.0078\) |
Rank
sage: E.rank()
The elliptic curves in class 18240p have rank \(0\).
Complex multiplication
The elliptic curves in class 18240p do not have complex multiplication.Modular form 18240.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
