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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 127050.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
127050.eg1 | 127050dk4 | \([1, 0, 1, -685226, 218175098]\) | \(1285429208617/614922\) | \(17021434894406250\) | \([2]\) | \(1966080\) | \(2.0693\) | |
127050.eg2 | 127050dk3 | \([1, 0, 1, -382726, -89648902]\) | \(223980311017/4278582\) | \(118433890726593750\) | \([2]\) | \(1966080\) | \(2.0693\) | |
127050.eg3 | 127050dk2 | \([1, 0, 1, -49976, 2190098]\) | \(498677257/213444\) | \(5908266657562500\) | \([2, 2]\) | \(983040\) | \(1.7228\) | |
127050.eg4 | 127050dk1 | \([1, 0, 1, 10524, 254098]\) | \(4657463/3696\) | \(-102307647750000\) | \([2]\) | \(491520\) | \(1.3762\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127050.eg have rank \(0\).
Complex multiplication
The elliptic curves in class 127050.eg do not have complex multiplication.Modular form 127050.2.a.eg
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.