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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 11088.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11088.bl1 | 11088bh5 | \([0, 0, 0, -650739, -202049678]\) | \(10206027697760497/5557167\) | \(16593611747328\) | \([2]\) | \(81920\) | \(1.8652\) | |
| 11088.bl2 | 11088bh3 | \([0, 0, 0, -40899, -3119870]\) | \(2533811507137/58110129\) | \(173515915431936\) | \([2, 2]\) | \(40960\) | \(1.5187\) | |
| 11088.bl3 | 11088bh2 | \([0, 0, 0, -5619, 90610]\) | \(6570725617/2614689\) | \(7807419518976\) | \([2, 2]\) | \(20480\) | \(1.1721\) | |
| 11088.bl4 | 11088bh1 | \([0, 0, 0, -4899, 131938]\) | \(4354703137/1617\) | \(4828336128\) | \([2]\) | \(10240\) | \(0.82552\) | \(\Gamma_0(N)\)-optimal |
| 11088.bl5 | 11088bh6 | \([0, 0, 0, 4461, -9660782]\) | \(3288008303/13504609503\) | \(-40324547902205952\) | \([2]\) | \(81920\) | \(1.8652\) | |
| 11088.bl6 | 11088bh4 | \([0, 0, 0, 18141, 656098]\) | \(221115865823/190238433\) | \(-568048917123072\) | \([2]\) | \(40960\) | \(1.5187\) |
Rank
sage: E.rank()
The elliptic curves in class 11088.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.bl do not have complex multiplication.Modular form 11088.2.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.
