Show commands:
SageMath
E = EllipticCurve("dg1")
E.isogeny_class()
Elliptic curves in class 51600dg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51600.dm2 | 51600dg1 | \([0, 1, 0, 6667, 1692963]\) | \(819200/31347\) | \(-1253880000000000\) | \([]\) | \(146880\) | \(1.5770\) | \(\Gamma_0(N)\)-optimal |
51600.dm1 | 51600dg2 | \([0, 1, 0, -893333, 324792963]\) | \(-1971080396800/715563\) | \(-28622520000000000\) | \([]\) | \(440640\) | \(2.1263\) |
Rank
sage: E.rank()
The elliptic curves in class 51600dg have rank \(0\).
Complex multiplication
The elliptic curves in class 51600dg do not have complex multiplication.Modular form 51600.2.a.dg
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.