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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 29040.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29040.u1 | 29040bt1 | \([0, -1, 0, -185456, -29934144]\) | \(129392980254539/3583180800\) | \(19534699089100800\) | \([2]\) | \(258048\) | \(1.9054\) | \(\Gamma_0(N)\)-optimal |
29040.u2 | 29040bt2 | \([0, -1, 0, 39824, -98239040]\) | \(1281177907381/765275040000\) | \(-4172108096471040000\) | \([2]\) | \(516096\) | \(2.2520\) |
Rank
sage: E.rank()
The elliptic curves in class 29040.u have rank \(0\).
Complex multiplication
The elliptic curves in class 29040.u do not have complex multiplication.Modular form 29040.2.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.