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SageMath
E = EllipticCurve("nw1")
E.isogeny_class()
Elliptic curves in class 100800nw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.ji3 | 100800nw1 | \([0, 0, 0, -1192575, -467381000]\) | \(257307998572864/19456203375\) | \(14183572260375000000\) | \([2]\) | \(1769472\) | \(2.4200\) | \(\Gamma_0(N)\)-optimal |
| 100800.ji2 | 100800nw2 | \([0, 0, 0, -3893700, 2406616000]\) | \(139927692143296/27348890625\) | \(1275989841000000000000\) | \([2, 2]\) | \(3538944\) | \(2.7666\) | |
| 100800.ji4 | 100800nw3 | \([0, 0, 0, 8013300, 14242174000]\) | \(152461584507448/322998046875\) | \(-120558375000000000000000\) | \([2]\) | \(7077888\) | \(3.1132\) | |
| 100800.ji1 | 100800nw4 | \([0, 0, 0, -59018700, 174506866000]\) | \(60910917333827912/3255076125\) | \(1214950653504000000000\) | \([2]\) | \(7077888\) | \(3.1132\) |
Rank
sage: E.rank()
The elliptic curves in class 100800nw have rank \(0\).
Complex multiplication
The elliptic curves in class 100800nw do not have complex multiplication.Modular form 100800.2.a.nw
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.
