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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 54080.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54080.n1 | 54080u1 | \([0, 1, 0, -9096481, -10561452225]\) | \(65787589563409/10400000\) | \(13159317792358400000\) | \([2]\) | \(2580480\) | \(2.6791\) | \(\Gamma_0(N)\)-optimal |
| 54080.n2 | 54080u2 | \([0, 1, 0, -8231201, -12650411201]\) | \(-48743122863889/26406250000\) | \(-33412330332160000000000\) | \([2]\) | \(5160960\) | \(3.0257\) |
Rank
sage: E.rank()
The elliptic curves in class 54080.n have rank \(1\).
Complex multiplication
The elliptic curves in class 54080.n do not have complex multiplication.Modular form 54080.2.a.n
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.
