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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 28050.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.u1 | 28050i1 | \([1, 1, 0, -22600, 1288000]\) | \(81706955619457/744505344\) | \(11632896000000\) | \([2]\) | \(143360\) | \(1.3293\) | \(\Gamma_0(N)\)-optimal |
28050.u2 | 28050i2 | \([1, 1, 0, -6600, 3096000]\) | \(-2035346265217/264305213568\) | \(-4129768962000000\) | \([2]\) | \(286720\) | \(1.6759\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.u have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.u do not have complex multiplication.Modular form 28050.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.