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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 32490.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32490.y1 | 32490x2 | \([1, -1, 0, -5258574, 4642679268]\) | \(468898230633769/5540400\) | \(190016036338359600\) | \([2]\) | \(1105920\) | \(2.4655\) | |
32490.y2 | 32490x1 | \([1, -1, 0, -320094, 76560660]\) | \(-105756712489/12476160\) | \(-427887963310083840\) | \([2]\) | \(552960\) | \(2.1189\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.y have rank \(0\).
Complex multiplication
The elliptic curves in class 32490.y 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 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.