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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 169338.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169338.u1 | 169338m1 | \([1, 1, 1, -854747, 301955753]\) | \(31434491726057626669/220590929608704\) | \(484638272350322688\) | \([2]\) | \(4874688\) | \(2.2264\) | \(\Gamma_0(N)\)-optimal |
| 169338.u2 | 169338m2 | \([1, 1, 1, -322267, 674478761]\) | \(-1684772434262416429/88512675985170432\) | \(-194462349139419439104\) | \([2]\) | \(9749376\) | \(2.5730\) |
Rank
sage: E.rank()
The elliptic curves in class 169338.u have rank \(0\).
Complex multiplication
The elliptic curves in class 169338.u do not have complex multiplication.Modular form 169338.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
