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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 160080.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.r1 | 160080cv3 | \([0, -1, 0, -94909896, 355921290000]\) | \(46166638840990604761819538/1182161275245\) | \(2421066291701760\) | \([2]\) | \(13369344\) | \(2.9192\) | |
| 160080.r2 | 160080cv4 | \([0, -1, 0, -6503416, 4426977616]\) | \(14853145385567267936498/4465637197701226875\) | \(9145624980892112640000\) | \([2]\) | \(13369344\) | \(2.9192\) | |
| 160080.r3 | 160080cv2 | \([0, -1, 0, -5932096, 5562304720]\) | \(22544901422512461142276/3607205401800225\) | \(3693778331443430400\) | \([2, 2]\) | \(6684672\) | \(2.5727\) | |
| 160080.r4 | 160080cv1 | \([0, -1, 0, -335276, 104285856]\) | \(-16281426076421404624/8891037713878335\) | \(-2276105654752853760\) | \([2]\) | \(3342336\) | \(2.2261\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 160080.r have rank \(0\).
Complex multiplication
The elliptic curves in class 160080.r do not have complex multiplication.Modular form 160080.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
