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SageMath
E = EllipticCurve("bu1")
E.isogeny_class()
Elliptic curves in class 32490.bu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.bu1 | 32490bv4 | \([1, -1, 1, -2017697, -1101035329]\) | \(26487576322129/44531250\) | \(1527263666557031250\) | \([2]\) | \(737280\) | \(2.3844\) | |
| 32490.bu2 | 32490bv2 | \([1, -1, 1, -165767, -5433541]\) | \(14688124849/8122500\) | \(278572892780002500\) | \([2, 2]\) | \(368640\) | \(2.0379\) | |
| 32490.bu3 | 32490bv1 | \([1, -1, 1, -100787, 12267011]\) | \(3301293169/22800\) | \(781958997277200\) | \([4]\) | \(184320\) | \(1.6913\) | \(\Gamma_0(N)\)-optimal |
| 32490.bu4 | 32490bv3 | \([1, -1, 1, 646483, -43446841]\) | \(871257511151/527800050\) | \(-18101666572844562450\) | \([2]\) | \(737280\) | \(2.3844\) |
Rank
sage: E.rank()
The elliptic curves in class 32490.bu have rank \(1\).
Complex multiplication
The elliptic curves in class 32490.bu do not have complex multiplication.Modular form 32490.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
