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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 27930cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27930.da2 | 27930cx1 | \([1, 0, 0, -1, 965]\) | \(-1/3420\) | \(-402359580\) | \([2]\) | \(17280\) | \(0.32995\) | \(\Gamma_0(N)\)-optimal |
27930.da1 | 27930cx2 | \([1, 0, 0, -1471, 21251]\) | \(2992209121/54150\) | \(6370693350\) | \([2]\) | \(34560\) | \(0.67653\) |
Rank
sage: E.rank()
The elliptic curves in class 27930cx have rank \(0\).
Complex multiplication
The elliptic curves in class 27930cx do not have complex multiplication.Modular form 27930.2.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 Cremona 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 Cremona labels.