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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 10164.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10164.u1 | 10164p4 | \([0, 1, 0, -221228, 39976836]\) | \(2640279346000/3087\) | \(1400015054592\) | \([2]\) | \(38880\) | \(1.6138\) | |
| 10164.u2 | 10164p3 | \([0, 1, 0, -13713, 631992]\) | \(-10061824000/352947\) | \(-10004274244272\) | \([2]\) | \(19440\) | \(1.2672\) | |
| 10164.u3 | 10164p2 | \([0, 1, 0, -3428, 23604]\) | \(9826000/5103\) | \(2314310600448\) | \([2]\) | \(12960\) | \(1.0645\) | |
| 10164.u4 | 10164p1 | \([0, 1, 0, 807, 3276]\) | \(2048000/1323\) | \(-37500403248\) | \([2]\) | \(6480\) | \(0.71788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10164.u have rank \(0\).
Complex multiplication
The elliptic curves in class 10164.u do not have complex multiplication.Modular form 10164.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
