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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 3360.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3360.k1 | 3360g3 | \([0, -1, 0, -14120, 650532]\) | \(608119035935048/826875\) | \(423360000\) | \([4]\) | \(3072\) | \(0.92955\) | |
| 3360.k2 | 3360g2 | \([0, -1, 0, -2240, -26520]\) | \(2428799546888/778248135\) | \(398463045120\) | \([2]\) | \(3072\) | \(0.92955\) | |
| 3360.k3 | 3360g1 | \([0, -1, 0, -890, 10200]\) | \(1219555693504/43758225\) | \(2800526400\) | \([2, 2]\) | \(1536\) | \(0.58297\) | \(\Gamma_0(N)\)-optimal |
| 3360.k4 | 3360g4 | \([0, -1, 0, 335, 34945]\) | \(1012048064/130203045\) | \(-533311672320\) | \([2]\) | \(3072\) | \(0.92955\) |
Rank
sage: E.rank()
The elliptic curves in class 3360.k have rank \(1\).
Complex multiplication
The elliptic curves in class 3360.k do not have complex multiplication.Modular form 3360.2.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.
