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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 257600dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.dy3 | 257600dy1 | \([0, 0, 0, -5900, 170000]\) | \(5545233/161\) | \(659456000000\) | \([2]\) | \(327680\) | \(1.0457\) | \(\Gamma_0(N)\)-optimal |
| 257600.dy2 | 257600dy2 | \([0, 0, 0, -13900, -390000]\) | \(72511713/25921\) | \(106172416000000\) | \([2, 2]\) | \(655360\) | \(1.3922\) | |
| 257600.dy4 | 257600dy3 | \([0, 0, 0, 42100, -2742000]\) | \(2014698447/1958887\) | \(-8023601152000000\) | \([2]\) | \(1310720\) | \(1.7388\) | |
| 257600.dy1 | 257600dy4 | \([0, 0, 0, -197900, -33878000]\) | \(209267191953/55223\) | \(226193408000000\) | \([2]\) | \(1310720\) | \(1.7388\) |
Rank
sage: E.rank()
The elliptic curves in class 257600dy have rank \(1\).
Complex multiplication
The elliptic curves in class 257600dy do not have complex multiplication.Modular form 257600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
