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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 20160bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.bh3 | 20160bd1 | \([0, 0, 0, -11388, 467728]\) | \(13674725584/945\) | \(11287019520\) | \([2]\) | \(24576\) | \(0.98263\) | \(\Gamma_0(N)\)-optimal |
| 20160.bh2 | 20160bd2 | \([0, 0, 0, -12108, 405232]\) | \(4108974916/893025\) | \(42664933785600\) | \([2, 2]\) | \(49152\) | \(1.3292\) | |
| 20160.bh1 | 20160bd3 | \([0, 0, 0, -62508, -5662928]\) | \(282678688658/18600435\) | \(1777299241697280\) | \([2]\) | \(98304\) | \(1.6758\) | |
| 20160.bh4 | 20160bd4 | \([0, 0, 0, 26772, 2473648]\) | \(22208984782/40516875\) | \(-3871447695360000\) | \([2]\) | \(98304\) | \(1.6758\) |
Rank
sage: E.rank()
The elliptic curves in class 20160bd have rank \(0\).
Complex multiplication
The elliptic curves in class 20160bd do not have complex multiplication.Modular form 20160.2.a.bd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
