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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 4598.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4598.p1 | 4598n3 | \([1, 0, 0, -10348, 3258256]\) | \(-69173457625/2550136832\) | \(-4517722956234752\) | \([]\) | \(19440\) | \(1.6841\) | |
| 4598.p2 | 4598n1 | \([1, 0, 0, -1878, -31492]\) | \(-413493625/152\) | \(-269277272\) | \([]\) | \(2160\) | \(0.58550\) | \(\Gamma_0(N)\)-optimal |
| 4598.p3 | 4598n2 | \([1, 0, 0, 1147, -118975]\) | \(94196375/3511808\) | \(-6221382092288\) | \([]\) | \(6480\) | \(1.1348\) |
Rank
sage: E.rank()
The elliptic curves in class 4598.p have rank \(1\).
Complex multiplication
The elliptic curves in class 4598.p do not have complex multiplication.Modular form 4598.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
