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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 204490.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
204490.cx1 | 204490bg1 | \([1, 0, 0, -20875, -3173015]\) | \(-117649/440\) | \(-3762434094693560\) | \([]\) | \(1105920\) | \(1.6743\) | \(\Gamma_0(N)\)-optimal |
204490.cx2 | 204490bg2 | \([1, 0, 0, 183615, 75310247]\) | \(80062991/332750\) | \(-2845340784112004750\) | \([]\) | \(3317760\) | \(2.2236\) |
Rank
sage: E.rank()
The elliptic curves in class 204490.cx have rank \(0\).
Complex multiplication
The elliptic curves in class 204490.cx do not have complex multiplication.Modular form 204490.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.