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SageMath
sage: E = EllipticCurve("gu1")
sage: E.isogeny_class()
Elliptic curves in class 212160.gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.gu1 | 212160p1 | \([0, 1, 0, -1124065, -458394337]\) | \(2396726313900986596/4154072495625\) | \(272241295073280000\) | \([2]\) | \(2949120\) | \(2.2393\) | \(\Gamma_0(N)\)-optimal |
| 212160.gu2 | 212160p2 | \([0, 1, 0, -772545, -749945025]\) | \(-389032340685029858/1627263833203125\) | \(-213288725145600000000\) | \([2]\) | \(5898240\) | \(2.5859\) |
Rank
sage: E.rank()
The elliptic curves in class 212160.gu have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.gu do not have complex multiplication.Modular form 212160.2.a.gu
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.
