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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 28224dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.ba1 | 28224dy1 | \([0, 0, 0, -1176, 13720]\) | \(55296/7\) | \(22769316864\) | \([2]\) | \(24576\) | \(0.71661\) | \(\Gamma_0(N)\)-optimal |
| 28224.ba2 | 28224dy2 | \([0, 0, 0, 1764, 71344]\) | \(11664/49\) | \(-2550163488768\) | \([2]\) | \(49152\) | \(1.0632\) |
Rank
sage: E.rank()
The elliptic curves in class 28224dy have rank \(1\).
Complex multiplication
The elliptic curves in class 28224dy do not have complex multiplication.Modular form 28224.2.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 Cremona 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 Cremona labels.
