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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 190463.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190463.u1 | 190463u1 | \([0, -1, 1, -361774807, -2648413697525]\) | \(-9221261135586623488/121324931\) | \(-68896697820895934171\) | \([]\) | \(27869184\) | \(3.3650\) | \(\Gamma_0(N)\)-optimal |
| 190463.u2 | 190463u2 | \([0, -1, 1, -341320737, -2961099479388]\) | \(-7743965038771437568/2189290237869371\) | \(-1243230609879542683233136211\) | \([]\) | \(83607552\) | \(3.9143\) |
Rank
sage: E.rank()
The elliptic curves in class 190463.u have rank \(0\).
Complex multiplication
The elliptic curves in class 190463.u do not have complex multiplication.Modular form 190463.2.a.u
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
