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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 48050.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48050.u1 | 48050v4 | \([1, 0, 0, -3015638, 2015446892]\) | \(-349938025/8\) | \(-69336225078125000\) | \([]\) | \(918000\) | \(2.3449\) | |
48050.u2 | 48050v3 | \([1, 0, 0, -12513, 6356267]\) | \(-25/2\) | \(-17334056269531250\) | \([]\) | \(306000\) | \(1.7956\) | |
48050.u3 | 48050v1 | \([1, 0, 0, -2903, -72823]\) | \(-121945/32\) | \(-710002944800\) | \([]\) | \(61200\) | \(0.99089\) | \(\Gamma_0(N)\)-optimal |
48050.u4 | 48050v2 | \([1, 0, 0, 21122, 537412]\) | \(46969655/32768\) | \(-727043015475200\) | \([]\) | \(183600\) | \(1.5402\) |
Rank
sage: E.rank()
The elliptic curves in class 48050.u have rank \(1\).
Complex multiplication
The elliptic curves in class 48050.u do not have complex multiplication.Modular form 48050.2.a.u
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.