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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 287490.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
287490.y1 | 287490y2 | \([1, 1, 0, -22896978167, 1333559082709269]\) | \(517425559361898728438440369/38638656000\) | \(99136220107466304000\) | \([2]\) | \(283668480\) | \(4.2052\) | |
287490.y2 | 287490y1 | \([1, 1, 0, -1431058167, 20836504213269]\) | \(-126323813482515646120369/1091629056000000\) | \(-2800821497810939904000000\) | \([2]\) | \(141834240\) | \(3.8586\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 287490.y have rank \(1\).
Complex multiplication
The elliptic curves in class 287490.y do not have complex multiplication.Modular form 287490.2.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.