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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 48672bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48672.r3 | 48672bu1 | \([0, 0, 0, -356421, 81508700]\) | \(22235451328/123201\) | \(27744816006333504\) | \([2, 2]\) | \(516096\) | \(1.9979\) | \(\Gamma_0(N)\)-optimal |
| 48672.r4 | 48672bu2 | \([0, 0, 0, -158691, 171475850]\) | \(-245314376/6908733\) | \(-12446751303764384256\) | \([2]\) | \(1032192\) | \(2.3445\) | |
| 48672.r2 | 48672bu3 | \([0, 0, 0, -561756, -23130016]\) | \(1360251712/771147\) | \(11114367774981599232\) | \([2]\) | \(1032192\) | \(2.3445\) | |
| 48672.r1 | 48672bu4 | \([0, 0, 0, -5695131, 5231228366]\) | \(11339065490696/351\) | \(632360478776832\) | \([2]\) | \(1032192\) | \(2.3445\) |
Rank
sage: E.rank()
The elliptic curves in class 48672bu have rank \(1\).
Complex multiplication
The elliptic curves in class 48672bu do not have complex multiplication.Modular form 48672.2.a.bu
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
