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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 22050.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.q1 | 22050y2 | \([1, -1, 0, -160092, 24820816]\) | \(-16591834777/98304\) | \(-2688505344000000\) | \([]\) | \(155520\) | \(1.8009\) | |
22050.q2 | 22050y1 | \([1, -1, 0, 5283, 179941]\) | \(596183/864\) | \(-23629441500000\) | \([]\) | \(51840\) | \(1.2516\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22050.q have rank \(0\).
Complex multiplication
The elliptic curves in class 22050.q do not have complex multiplication.Modular form 22050.2.a.q
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.