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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 173280.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173280.k1 | 173280bh4 | \([0, -1, 0, -29361, -1924959]\) | \(14526784/15\) | \(2890498928640\) | \([2]\) | \(387072\) | \(1.3090\) | |
| 173280.k2 | 173280bh2 | \([0, -1, 0, -20336, 1112856]\) | \(38614472/405\) | \(9755433884160\) | \([2]\) | \(387072\) | \(1.3090\) | |
| 173280.k3 | 173280bh1 | \([0, -1, 0, -2286, -13464]\) | \(438976/225\) | \(677460686400\) | \([2, 2]\) | \(193536\) | \(0.96238\) | \(\Gamma_0(N)\)-optimal |
| 173280.k4 | 173280bh3 | \([0, -1, 0, 8544, -113100]\) | \(2863288/1875\) | \(-45164045760000\) | \([2]\) | \(387072\) | \(1.3090\) |
Rank
sage: E.rank()
The elliptic curves in class 173280.k have rank \(1\).
Complex multiplication
The elliptic curves in class 173280.k do not have complex multiplication.Modular form 173280.2.a.k
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.
