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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 166410u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.cl2 | 166410u1 | \([1, -1, 1, -170670443, -889883315269]\) | \(-119305480789133569/5200091136000\) | \(-23963443025777725741056000\) | \([2]\) | \(74511360\) | \(3.6353\) | \(\Gamma_0(N)\)-optimal |
166410.cl1 | 166410u2 | \([1, -1, 1, -2758678763, -55769117342533]\) | \(503835593418244309249/898614000000\) | \(4141059229152368694000000\) | \([2]\) | \(149022720\) | \(3.9819\) |
Rank
sage: E.rank()
The elliptic curves in class 166410u have rank \(0\).
Complex multiplication
The elliptic curves in class 166410u do not have complex multiplication.Modular form 166410.2.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 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.