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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 51744bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51744.cr3 | 51744bq1 | \([0, 1, 0, -1682, 22560]\) | \(69934528/9801\) | \(73796982336\) | \([2, 2]\) | \(49152\) | \(0.81160\) | \(\Gamma_0(N)\)-optimal |
| 51744.cr4 | 51744bq2 | \([0, 1, 0, 2728, 124872]\) | \(37259704/131769\) | \(-7937275433472\) | \([2]\) | \(98304\) | \(1.1582\) | |
| 51744.cr2 | 51744bq3 | \([0, 1, 0, -7072, -208132]\) | \(649461896/72171\) | \(4347313141248\) | \([2]\) | \(98304\) | \(1.1582\) | |
| 51744.cr1 | 51744bq4 | \([0, 1, 0, -25937, 1599135]\) | \(4004529472/99\) | \(47707140096\) | \([2]\) | \(98304\) | \(1.1582\) |
Rank
sage: E.rank()
The elliptic curves in class 51744bq have rank \(0\).
Complex multiplication
The elliptic curves in class 51744bq do not have complex multiplication.Modular form 51744.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
