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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 17160e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.m2 | 17160e1 | \([0, -1, 0, -1600, 25852]\) | \(-442644537604/14274975\) | \(-14617574400\) | \([2]\) | \(11264\) | \(0.72601\) | \(\Gamma_0(N)\)-optimal |
| 17160.m1 | 17160e2 | \([0, -1, 0, -25800, 1603692]\) | \(927405593024402/920205\) | \(1884579840\) | \([2]\) | \(22528\) | \(1.0726\) |
Rank
sage: E.rank()
The elliptic curves in class 17160e have rank \(1\).
Complex multiplication
The elliptic curves in class 17160e do not have complex multiplication.Modular form 17160.2.a.e
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.
