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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 1850.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1850.f1 | 1850a3 | \([1, 1, 0, -131875, -18487875]\) | \(16232905099479601/4052240\) | \(63316250000\) | \([2]\) | \(6912\) | \(1.4482\) | |
| 1850.f2 | 1850a4 | \([1, 1, 0, -131375, -18634375]\) | \(-16048965315233521/256572640900\) | \(-4008947514062500\) | \([2]\) | \(13824\) | \(1.7948\) | |
| 1850.f3 | 1850a1 | \([1, 1, 0, -1875, -17875]\) | \(46694890801/18944000\) | \(296000000000\) | \([2]\) | \(2304\) | \(0.89892\) | \(\Gamma_0(N)\)-optimal |
| 1850.f4 | 1850a2 | \([1, 1, 0, 6125, -121875]\) | \(1625964918479/1369000000\) | \(-21390625000000\) | \([2]\) | \(4608\) | \(1.2455\) |
Rank
sage: E.rank()
The elliptic curves in class 1850.f have rank \(1\).
Complex multiplication
The elliptic curves in class 1850.f do not have complex multiplication.Modular form 1850.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
