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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 235950.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235950.y1 | 235950y2 | \([1, 1, 0, -1485200, -444096000]\) | \(139370512222423/47971512576\) | \(124707193825500000000\) | \([2]\) | \(7864320\) | \(2.5579\) | |
235950.y2 | 235950y1 | \([1, 1, 0, 274800, -48096000]\) | \(882802050857/897122304\) | \(-2332167552000000000\) | \([2]\) | \(3932160\) | \(2.2113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235950.y have rank \(2\).
Complex multiplication
The elliptic curves in class 235950.y do not have complex multiplication.Modular form 235950.2.a.y
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.