Show commands:
SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 102960.dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dy1 | 102960er2 | \([0, 0, 0, -79493547, -272802143014]\) | \(-18605093748570727251049/91759078125000\) | \(-273991139136000000000\) | \([]\) | \(8709120\) | \(3.1211\) | |
| 102960.dy2 | 102960er1 | \([0, 0, 0, -586587, -677442166]\) | \(-7475384530020889/62069784455250\) | \(-185339383266825216000\) | \([]\) | \(2903040\) | \(2.5718\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.dy have rank \(0\).
Complex multiplication
The elliptic curves in class 102960.dy do not have complex multiplication.Modular form 102960.2.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.
