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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 32490y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.o2 | 32490y1 | \([1, -1, 0, -255114, -173898252]\) | \(-53540005609/350208000\) | \(-12010890198177792000\) | \([2]\) | \(967680\) | \(2.3445\) | \(\Gamma_0(N)\)-optimal |
| 32490.o1 | 32490y2 | \([1, -1, 0, -6493194, -6353340300]\) | \(882774443450089/2166000000\) | \(74286104741334000000\) | \([2]\) | \(1935360\) | \(2.6910\) |
Rank
sage: E.rank()
The elliptic curves in class 32490y have rank \(0\).
Complex multiplication
The elliptic curves in class 32490y do not have complex multiplication.Modular form 32490.2.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 Cremona 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 Cremona labels.
