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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 179088cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179088.l4 | 179088cb1 | \([0, -1, 0, 1596, -220896]\) | \(1755133942448/82961251191\) | \(-21238080304896\) | \([2]\) | \(448512\) | \(1.2370\) | \(\Gamma_0(N)\)-optimal |
| 179088.l3 | 179088cb2 | \([0, -1, 0, -46424, -3678336]\) | \(10805895991757668/497249215281\) | \(509183196447744\) | \([2, 2]\) | \(897024\) | \(1.5836\) | |
| 179088.l2 | 179088cb3 | \([0, -1, 0, -126784, 12586528]\) | \(110050123396493954/30493579179609\) | \(62450850159839232\) | \([2]\) | \(1794048\) | \(1.9301\) | |
| 179088.l1 | 179088cb4 | \([0, -1, 0, -734384, -241987680]\) | \(21387694409289325154/48600263439\) | \(99533339523072\) | \([2]\) | \(1794048\) | \(1.9301\) |
Rank
sage: E.rank()
The elliptic curves in class 179088cb have rank \(1\).
Complex multiplication
The elliptic curves in class 179088cb do not have complex multiplication.Modular form 179088.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
