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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 10350.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.y1 | 10350e4 | \([1, -1, 0, -884292, -285025384]\) | \(248656466619387/29607177800\) | \(9105595009959375000\) | \([2]\) | \(248832\) | \(2.3690\) | |
10350.y2 | 10350e3 | \([1, -1, 0, -857292, -305302384]\) | \(226568219476347/3893440\) | \(1197415305000000\) | \([2]\) | \(124416\) | \(2.0224\) | |
10350.y3 | 10350e2 | \([1, -1, 0, -209292, 36849616]\) | \(2403250125069123/4232000000\) | \(1785375000000000\) | \([2]\) | \(82944\) | \(1.8197\) | |
10350.y4 | 10350e1 | \([1, -1, 0, -17292, 177616]\) | \(1355469437763/753664000\) | \(317952000000000\) | \([2]\) | \(41472\) | \(1.4731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10350.y have rank \(0\).
Complex multiplication
The elliptic curves in class 10350.y do not have complex multiplication.Modular form 10350.2.a.y
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.