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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 209814.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209814.n1 | 209814cv1 | \([1, 1, 0, -6924590, -7016188032]\) | \(858729462625/38148\) | \(1631253337287472932\) | \([2]\) | \(8847360\) | \(2.5720\) | \(\Gamma_0(N)\)-optimal |
209814.n2 | 209814cv2 | \([1, 1, 0, -6574900, -7756062134]\) | \(-735091890625/181908738\) | \(-7778631538855314676242\) | \([2]\) | \(17694720\) | \(2.9186\) |
Rank
sage: E.rank()
The elliptic curves in class 209814.n have rank \(0\).
Complex multiplication
The elliptic curves in class 209814.n do not have complex multiplication.Modular form 209814.2.a.n
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.