Show commands:
SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 487872.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.dy1 | 487872dy1 | \([0, 0, 0, -2313036, -1352956176]\) | \(598885164/539\) | \(1231731645012836352\) | \([2]\) | \(10321920\) | \(2.3957\) | \(\Gamma_0(N)\)-optimal |
| 487872.dy2 | 487872dy2 | \([0, 0, 0, -1790316, -1980847440]\) | \(-138853062/290521\) | \(-1327806713323837587456\) | \([2]\) | \(20643840\) | \(2.7422\) |
Rank
sage: E.rank()
The elliptic curves in class 487872.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 487872.dy do not have complex multiplication.Modular form 487872.2.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.
