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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 481338cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.cy1 | 481338cy1 | \([1, -1, 1, -91844105, -338741481207]\) | \(66342819962001390625/4812668669952\) | \(6215407432652840767488\) | \([2]\) | \(56770560\) | \(3.2329\) | \(\Gamma_0(N)\)-optimal |
481338.cy2 | 481338cy2 | \([1, -1, 1, -85919945, -384336186231]\) | \(-54315282059491182625/17983956399469632\) | \(-23225703645807598316217408\) | \([2]\) | \(113541120\) | \(3.5795\) |
Rank
sage: E.rank()
The elliptic curves in class 481338cy have rank \(1\).
Complex multiplication
The elliptic curves in class 481338cy do not have complex multiplication.Modular form 481338.2.a.cy
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.