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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 18240.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18240.k1 | 18240bu3 | \([0, -1, 0, -121601, -16280799]\) | \(3034301922374404/1425\) | \(93388800\) | \([2]\) | \(32768\) | \(1.3030\) | |
| 18240.k2 | 18240bu4 | \([0, -1, 0, -9121, -142655]\) | \(1280615525284/601171875\) | \(39398400000000\) | \([2]\) | \(32768\) | \(1.3030\) | |
| 18240.k3 | 18240bu2 | \([0, -1, 0, -7601, -252399]\) | \(2964647793616/2030625\) | \(33269760000\) | \([2, 2]\) | \(16384\) | \(0.95645\) | |
| 18240.k4 | 18240bu1 | \([0, -1, 0, -381, -5475]\) | \(-5988775936/9774075\) | \(-10008652800\) | \([2]\) | \(8192\) | \(0.60988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18240.k have rank \(1\).
Complex multiplication
The elliptic curves in class 18240.k do not have complex multiplication.Modular form 18240.2.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.
