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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 289800.bz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.bz1 | 289800bz3 | \([0, 0, 0, -41733075, 103769252750]\) | \(344577854816148242/2716875\) | \(63379260000000000\) | \([2]\) | \(11796480\) | \(2.8149\) | |
| 289800.bz2 | 289800bz2 | \([0, 0, 0, -2610075, 1619099750]\) | \(168591300897604/472410225\) | \(5510192864400000000\) | \([2, 2]\) | \(5898240\) | \(2.4684\) | |
| 289800.bz3 | 289800bz4 | \([0, 0, 0, -1575075, 2915954750]\) | \(-18524646126002/146738831715\) | \(-3423123466247520000000\) | \([2]\) | \(11796480\) | \(2.8149\) | |
| 289800.bz4 | 289800bz1 | \([0, 0, 0, -229575, 2740250]\) | \(458891455696/264449745\) | \(771135456420000000\) | \([2]\) | \(2949120\) | \(2.1218\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 289800.bz have rank \(0\).
Complex multiplication
The elliptic curves in class 289800.bz do not have complex multiplication.Modular form 289800.2.a.bz
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.
