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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 169065r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169065.t2 | 169065r1 | \([0, 0, 1, 3468, -101945]\) | \(7077888/10985\) | \(-7159082277555\) | \([]\) | \(241920\) | \(1.1519\) | \(\Gamma_0(N)\)-optimal |
| 169065.t1 | 169065r2 | \([0, 0, 1, -109242, -13961518]\) | \(-303464448/1625\) | \(-772037127268875\) | \([]\) | \(725760\) | \(1.7012\) |
Rank
sage: E.rank()
The elliptic curves in class 169065r have rank \(1\).
Complex multiplication
The elliptic curves in class 169065r do not have complex multiplication.Modular form 169065.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
