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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 46800.dy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46800.dy1 | 46800cj2 | \([0, 0, 0, -285099075, 927527645250]\) | \(2034416504287874043/882294347833600\) | \(1111436777498159923200000000\) | \([2]\) | \(17694720\) | \(3.8858\) | |
46800.dy2 | 46800cj1 | \([0, 0, 0, 60500925, 107418845250]\) | \(19441890357117957/15208161280000\) | \(-19157903262351360000000000\) | \([2]\) | \(8847360\) | \(3.5392\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46800.dy have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.dy do not have complex multiplication.Modular form 46800.2.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.