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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 258570r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 258570.r2 | 258570r1 | \([1, -1, 0, -3015, -48515]\) | \(1892819053/440640\) | \(705734752320\) | \([2]\) | \(405504\) | \(0.98552\) | \(\Gamma_0(N)\)-optimal |
| 258570.r1 | 258570r2 | \([1, -1, 0, -45135, -3679259]\) | \(6349095794413/520200\) | \(833159082600\) | \([2]\) | \(811008\) | \(1.3321\) |
Rank
sage: E.rank()
The elliptic curves in class 258570r have rank \(1\).
Complex multiplication
The elliptic curves in class 258570r do not have complex multiplication.Modular form 258570.2.a.r
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.
