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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 17136be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17136.i1 | 17136be1 | \([0, 0, 0, -516, -4345]\) | \(1302642688/54621\) | \(637099344\) | \([2]\) | \(6912\) | \(0.45414\) | \(\Gamma_0(N)\)-optimal |
| 17136.i2 | 17136be2 | \([0, 0, 0, 249, -16126]\) | \(9148592/607257\) | \(-113328730368\) | \([2]\) | \(13824\) | \(0.80072\) |
Rank
sage: E.rank()
The elliptic curves in class 17136be have rank \(0\).
Complex multiplication
The elliptic curves in class 17136be do not have complex multiplication.Modular form 17136.2.a.be
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.
