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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 138600.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
138600.cx1 | 138600f2 | \([0, 0, 0, -100875, 9593750]\) | \(77860436/17787\) | \(25933446000000000\) | \([2]\) | \(737280\) | \(1.8620\) | |
138600.cx2 | 138600f1 | \([0, 0, 0, -33375, -2218750]\) | \(11279504/693\) | \(252598500000000\) | \([2]\) | \(368640\) | \(1.5154\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 138600.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 138600.cx do not have complex multiplication.Modular form 138600.2.a.cx
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.