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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 16560.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.bq1 | 16560br3 | \([0, 0, 0, -199067187, -1081054609166]\) | \(292169767125103365085489/72534787200\) | \(216587714022604800\) | \([2]\) | \(1376256\) | \(3.1421\) | |
| 16560.bq2 | 16560br4 | \([0, 0, 0, -14562867, -10741436174]\) | \(114387056741228939569/49503729150000000\) | \(147817343182233600000000\) | \([2]\) | \(1376256\) | \(3.1421\) | |
| 16560.bq3 | 16560br2 | \([0, 0, 0, -12443187, -16887236366]\) | \(71356102305927901489/35540674560000\) | \(106123885585367040000\) | \([2, 2]\) | \(688128\) | \(2.7955\) | |
| 16560.bq4 | 16560br1 | \([0, 0, 0, -646707, -355649294]\) | \(-10017490085065009/12502381363200\) | \(-37331910712413388800\) | \([2]\) | \(344064\) | \(2.4489\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.bq have rank \(0\).
Complex multiplication
The elliptic curves in class 16560.bq do not have complex multiplication.Modular form 16560.2.a.bq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
