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SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 54450gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54450.fz2 | 54450gu1 | \([1, -1, 1, -1805, -14803]\) | \(18865/8\) | \(275653125000\) | \([]\) | \(69120\) | \(0.89192\) | \(\Gamma_0(N)\)-optimal |
| 54450.fz1 | 54450gu2 | \([1, -1, 1, -125555, -17092303]\) | \(6352571665/2\) | \(68913281250\) | \([]\) | \(207360\) | \(1.4412\) |
Rank
sage: E.rank()
The elliptic curves in class 54450gu have rank \(1\).
Complex multiplication
The elliptic curves in class 54450gu do not have complex multiplication.Modular form 54450.2.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 Cremona 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 Cremona labels.
