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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 162288.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162288.dr1 | 162288bp2 | \([0, 0, 0, -4272555, -3182362918]\) | \(24553362849625/1755162752\) | \(616585219943321567232\) | \([2]\) | \(6193152\) | \(2.7362\) | |
162288.dr2 | 162288bp1 | \([0, 0, 0, 243285, -217262374]\) | \(4533086375/60669952\) | \(-21313234715837202432\) | \([2]\) | \(3096576\) | \(2.3896\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162288.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 162288.dr do not have complex multiplication.Modular form 162288.2.a.dr
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.