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SageMath
E = EllipticCurve("du1")
E.isogeny_class()
Elliptic curves in class 19600du
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.co2 | 19600du1 | \([0, 1, 0, 87792, 8429588]\) | \(397535/392\) | \(-73789452800000000\) | \([]\) | \(138240\) | \(1.9236\) | \(\Gamma_0(N)\)-optimal |
19600.co1 | 19600du2 | \([0, 1, 0, -892208, -456090412]\) | \(-417267265/235298\) | \(-44292119043200000000\) | \([]\) | \(414720\) | \(2.4730\) |
Rank
sage: E.rank()
The elliptic curves in class 19600du have rank \(0\).
Complex multiplication
The elliptic curves in class 19600du do not have complex multiplication.Modular form 19600.2.a.du
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.