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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 33810.cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.cx1 | 33810cw1 | \([1, 0, 0, -253086, 48949956]\) | \(15238420194810961/12619514880\) | \(1484673306117120\) | \([2]\) | \(322560\) | \(1.8395\) | \(\Gamma_0(N)\)-optimal |
33810.cx2 | 33810cw2 | \([1, 0, 0, -198206, 70781220]\) | \(-7319577278195281/14169067365600\) | \(-1666976606495474400\) | \([2]\) | \(645120\) | \(2.1861\) |
Rank
sage: E.rank()
The elliptic curves in class 33810.cx have rank \(1\).
Complex multiplication
The elliptic curves in class 33810.cx do not have complex multiplication.Modular form 33810.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.