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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 55440dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55440.db3 | 55440dy1 | \([0, 0, 0, -23952, 1447931]\) | \(-130287139815424/2250652635\) | \(-26251612334640\) | \([2]\) | \(165888\) | \(1.3728\) | \(\Gamma_0(N)\)-optimal |
| 55440.db2 | 55440dy2 | \([0, 0, 0, -384807, 91878194]\) | \(33766427105425744/9823275\) | \(1833258873600\) | \([2]\) | \(331776\) | \(1.7194\) | |
| 55440.db4 | 55440dy3 | \([0, 0, 0, 92688, 6938759]\) | \(7549996227362816/6152409907875\) | \(-71761709165454000\) | \([2]\) | \(497664\) | \(1.9222\) | |
| 55440.db1 | 55440dy4 | \([0, 0, 0, -446367, 60520826]\) | \(52702650535889104/22020583921875\) | \(4109569453836000000\) | \([2]\) | \(995328\) | \(2.2687\) |
Rank
sage: E.rank()
The elliptic curves in class 55440dy have rank \(0\).
Complex multiplication
The elliptic curves in class 55440dy do not have complex multiplication.Modular form 55440.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
