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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 20800.dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20800.dx1 | 20800df2 | \([0, -1, 0, -725153, 237921857]\) | \(-6434774386429585/140608\) | \(-921488588800\) | \([]\) | \(207360\) | \(1.8221\) | |
20800.dx2 | 20800df1 | \([0, -1, 0, -8353, 374337]\) | \(-9836106385/3407872\) | \(-22333829939200\) | \([]\) | \(69120\) | \(1.2728\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20800.dx have rank \(1\).
Complex multiplication
The elliptic curves in class 20800.dx do not have complex multiplication.Modular form 20800.2.a.dx
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 LMFDB 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 LMFDB labels.