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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 185130dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 185130.g1 | 185130dy1 | \([1, -1, 0, -2745, 232821]\) | \(-1771561/17000\) | \(-21954955473000\) | \([]\) | \(518400\) | \(1.2424\) | \(\Gamma_0(N)\)-optimal |
| 185130.g2 | 185130dy2 | \([1, -1, 0, 24480, -5958144]\) | \(1256216039/12577280\) | \(-16243154257144320\) | \([]\) | \(1555200\) | \(1.7917\) |
Rank
sage: E.rank()
The elliptic curves in class 185130dy have rank \(1\).
Complex multiplication
The elliptic curves in class 185130dy do not have complex multiplication.Modular form 185130.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
