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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 5880.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5880.bj1 | 5880p3 | \([0, 1, 0, -85080, -9020880]\) | \(282678688658/18600435\) | \(4481684638341120\) | \([2]\) | \(36864\) | \(1.7529\) | |
| 5880.bj2 | 5880p2 | \([0, 1, 0, -16480, 638000]\) | \(4108974916/893025\) | \(107585022182400\) | \([2, 2]\) | \(18432\) | \(1.4063\) | |
| 5880.bj3 | 5880p1 | \([0, 1, 0, -15500, 737568]\) | \(13674725584/945\) | \(28461646080\) | \([2]\) | \(9216\) | \(1.0597\) | \(\Gamma_0(N)\)-optimal |
| 5880.bj4 | 5880p4 | \([0, 1, 0, 36440, 3940208]\) | \(22208984782/40516875\) | \(-9762344605440000\) | \([2]\) | \(36864\) | \(1.7529\) |
Rank
sage: E.rank()
The elliptic curves in class 5880.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 5880.bj do not have complex multiplication.Modular form 5880.2.a.bj
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.
