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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 17160r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17160.g3 | 17160r1 | \([0, -1, 0, -11791, -488384]\) | \(11331632459167744/13573828125\) | \(217181250000\) | \([2]\) | \(25600\) | \(1.0863\) | \(\Gamma_0(N)\)-optimal |
| 17160.g2 | 17160r2 | \([0, -1, 0, -14916, -205884]\) | \(1433738629147984/754683125625\) | \(193198880160000\) | \([2, 2]\) | \(51200\) | \(1.4329\) | |
| 17160.g1 | 17160r3 | \([0, -1, 0, -136416, 19282716]\) | \(274171855990660996/2540331726075\) | \(2601299687500800\) | \([4]\) | \(102400\) | \(1.7794\) | |
| 17160.g4 | 17160r4 | \([0, -1, 0, 56584, -1664484]\) | \(19565773220287004/12465254233575\) | \(-12764420335180800\) | \([2]\) | \(102400\) | \(1.7794\) |
Rank
sage: E.rank()
The elliptic curves in class 17160r have rank \(0\).
Complex multiplication
The elliptic curves in class 17160r do not have complex multiplication.Modular form 17160.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
