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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 32144.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32144.y1 | 32144v1 | \([0, 1, 0, -44, 104]\) | \(-768208/41\) | \(-514304\) | \([]\) | \(4608\) | \(-0.14519\) | \(\Gamma_0(N)\)-optimal |
32144.y2 | 32144v2 | \([0, 1, 0, 236, 328]\) | \(115393712/68921\) | \(-864545024\) | \([]\) | \(13824\) | \(0.40411\) |
Rank
sage: E.rank()
The elliptic curves in class 32144.y have rank \(0\).
Complex multiplication
The elliptic curves in class 32144.y do not have complex multiplication.Modular form 32144.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.