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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 227430.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
227430.x1 | 227430fy2 | \([1, -1, 0, -22789095, -40428144379]\) | \(1413487789441083/55278125000\) | \(51187769048325459375000\) | \([2]\) | \(26542080\) | \(3.1247\) | |
227430.x2 | 227430fy1 | \([1, -1, 0, -3684975, 1872198125]\) | \(5976054062523/1824760000\) | \(1689735197216301480000\) | \([2]\) | \(13271040\) | \(2.7781\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 227430.x have rank \(1\).
Complex multiplication
The elliptic curves in class 227430.x do not have complex multiplication.Modular form 227430.2.a.x
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.