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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 103488.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.bl1 | 103488cb6 | \([0, -1, 0, -14171649, 20538957825]\) | \(10206027697760497/5557167\) | \(171388473280561152\) | \([2]\) | \(3932160\) | \(2.6355\) | |
| 103488.bl2 | 103488cb4 | \([0, -1, 0, -890689, 317368129]\) | \(2533811507137/58110129\) | \(1792173294674509824\) | \([2, 2]\) | \(1966080\) | \(2.2889\) | |
| 103488.bl3 | 103488cb2 | \([0, -1, 0, -122369, -9167871]\) | \(6570725617/2614689\) | \(80639569732829184\) | \([2, 2]\) | \(983040\) | \(1.9423\) | |
| 103488.bl4 | 103488cb1 | \([0, -1, 0, -106689, -13373247]\) | \(4354703137/1617\) | \(49869863780352\) | \([2]\) | \(491520\) | \(1.5957\) | \(\Gamma_0(N)\)-optimal |
| 103488.bl5 | 103488cb5 | \([0, -1, 0, 97151, 981789313]\) | \(3288008303/13504609503\) | \(-416495384243325370368\) | \([2]\) | \(3932160\) | \(2.6355\) | |
| 103488.bl6 | 103488cb3 | \([0, -1, 0, 395071, -66810687]\) | \(221115865823/190238433\) | \(-5867139603894632448\) | \([2]\) | \(1966080\) | \(2.2889\) |
Rank
sage: E.rank()
The elliptic curves in class 103488.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 103488.bl do not have complex multiplication.Modular form 103488.2.a.bl
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
