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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 43120.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43120.k1 | 43120bw4 | \([0, 1, 0, -347916, -79103816]\) | \(154639330142416/33275\) | \(1002181241600\) | \([2]\) | \(248832\) | \(1.6874\) | |
| 43120.k2 | 43120bw3 | \([0, 1, 0, -21821, -1232330]\) | \(610462990336/8857805\) | \(16673790407120\) | \([2]\) | \(124416\) | \(1.3408\) | |
| 43120.k3 | 43120bw2 | \([0, 1, 0, -4916, -76616]\) | \(436334416/171875\) | \(5176556000000\) | \([2]\) | \(82944\) | \(1.1381\) | |
| 43120.k4 | 43120bw1 | \([0, 1, 0, -2221, 38730]\) | \(643956736/15125\) | \(28471058000\) | \([2]\) | \(41472\) | \(0.79153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43120.k have rank \(0\).
Complex multiplication
The elliptic curves in class 43120.k do not have complex multiplication.Modular form 43120.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
