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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 48400.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.cx1 | 48400ch2 | \([0, -1, 0, -1453008, -673679488]\) | \(-24729001\) | \(-13718968384000000\) | \([]\) | \(591360\) | \(2.1789\) | |
48400.cx2 | 48400ch1 | \([0, -1, 0, -1008, 48512]\) | \(-121\) | \(-937024000000\) | \([]\) | \(53760\) | \(0.97991\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48400.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 48400.cx do not have complex multiplication.Modular form 48400.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.