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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 8450.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8450.y1 | 8450t2 | \([1, -1, 1, -898605, -359508353]\) | \(-1064019559329/125497034\) | \(-9464847081007906250\) | \([]\) | \(329280\) | \(2.3770\) | |
8450.y2 | 8450t1 | \([1, -1, 1, -11355, 715147]\) | \(-2146689/1664\) | \(-125497034000000\) | \([]\) | \(47040\) | \(1.4040\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8450.y have rank \(0\).
Complex multiplication
The elliptic curves in class 8450.y do not have complex multiplication.Modular form 8450.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.