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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 37200.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37200.dy1 | 37200cx2 | \([0, 1, 0, -87379008, -314411928012]\) | \(1152829477932246539641/3188367360\) | \(204055511040000000\) | \([2]\) | \(2396160\) | \(2.9796\) | |
37200.dy2 | 37200cx1 | \([0, 1, 0, -5459008, -4918168012]\) | \(-281115640967896441/468084326400\) | \(-29957396889600000000\) | \([2]\) | \(1198080\) | \(2.6330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37200.dy have rank \(1\).
Complex multiplication
The elliptic curves in class 37200.dy do not have complex multiplication.Modular form 37200.2.a.dy
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.