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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 14490.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14490.bb1 | 14490ba3 | \([1, -1, 0, -15219, 720225]\) | \(534774372149809/5323062500\) | \(3880512562500\) | \([6]\) | \(41472\) | \(1.2342\) | |
| 14490.bb2 | 14490ba4 | \([1, -1, 0, -3969, 1752975]\) | \(-9486391169809/1813439640250\) | \(-1321997497742250\) | \([6]\) | \(82944\) | \(1.5808\) | |
| 14490.bb3 | 14490ba1 | \([1, -1, 0, -1359, -18387]\) | \(380920459249/12622400\) | \(9201729600\) | \([2]\) | \(13824\) | \(0.68492\) | \(\Gamma_0(N)\)-optimal |
| 14490.bb4 | 14490ba2 | \([1, -1, 0, 441, -64827]\) | \(12994449551/2489452840\) | \(-1814811120360\) | \([2]\) | \(27648\) | \(1.0315\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 14490.bb do not have complex multiplication.Modular form 14490.2.a.bb
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.
