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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 209814e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209814.cw2 | 209814e1 | \([1, 0, 0, -9250029, 534497745]\) | \(2046931732873/1181672448\) | \(50529703375816761541632\) | \([2]\) | \(16588800\) | \(3.0459\) | \(\Gamma_0(N)\)-optimal |
209814.cw1 | 209814e2 | \([1, 0, 0, -104365709, 409322667249]\) | \(2940001530995593/8673562656\) | \(370891738197860898595104\) | \([2]\) | \(33177600\) | \(3.3925\) |
Rank
sage: E.rank()
The elliptic curves in class 209814e have rank \(0\).
Complex multiplication
The elliptic curves in class 209814e do not have complex multiplication.Modular form 209814.2.a.e
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.