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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 61710.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.u1 | 61710u2 | \([1, 0, 1, -7509439, -7921248238]\) | \(35185850652034529726579/26967168000\) | \(35893300608000\) | \([2]\) | \(2073600\) | \(2.3425\) | |
61710.u2 | 61710u1 | \([1, 0, 1, -469439, -123744238]\) | \(8595711443128766579/7520256000000\) | \(10009460736000000\) | \([2]\) | \(1036800\) | \(1.9959\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61710.u have rank \(0\).
Complex multiplication
The elliptic curves in class 61710.u do not have complex multiplication.Modular form 61710.2.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.