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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 58800.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.dy1 | 58800ft1 | \([0, -1, 0, -806458, 297495787]\) | \(-3155449600/250047\) | \(-4596528047343750000\) | \([]\) | \(1244160\) | \(2.3279\) | \(\Gamma_0(N)\)-optimal |
| 58800.dy2 | 58800ft2 | \([0, -1, 0, 4706042, 115583287]\) | \(627021958400/363182463\) | \(-6676258373357343750000\) | \([]\) | \(3732480\) | \(2.8772\) |
Rank
sage: E.rank()
The elliptic curves in class 58800.dy have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.dy do not have complex multiplication.Modular form 58800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
