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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 172062.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 172062.f1 | 172062y3 | \([1, -1, 0, -5680791, -5210057187]\) | \(15698803397448457/20709376\) | \(26745495761977344\) | \([]\) | \(5184000\) | \(2.4281\) | |
| 172062.f2 | 172062y2 | \([1, -1, 0, -88776, -3030912]\) | \(59914169497/31554496\) | \(40751620861938624\) | \([]\) | \(1728000\) | \(1.8788\) | |
| 172062.f3 | 172062y1 | \([1, -1, 0, -50661, 4401513]\) | \(11134383337/316\) | \(408103878204\) | \([]\) | \(576000\) | \(1.3295\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 172062.f have rank \(1\).
Complex multiplication
The elliptic curves in class 172062.f do not have complex multiplication.Modular form 172062.2.a.f
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
