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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 10080.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10080.q1 | 10080u3 | \([0, 0, 0, -6123, 184322]\) | \(68017239368/39375\) | \(14696640000\) | \([2]\) | \(8192\) | \(0.89650\) | |
| 10080.q2 | 10080u2 | \([0, 0, 0, -3603, -82042]\) | \(13858588808/229635\) | \(85710804480\) | \([2]\) | \(8192\) | \(0.89650\) | |
| 10080.q3 | 10080u1 | \([0, 0, 0, -453, 1748]\) | \(220348864/99225\) | \(4629441600\) | \([2, 2]\) | \(4096\) | \(0.54992\) | \(\Gamma_0(N)\)-optimal |
| 10080.q4 | 10080u4 | \([0, 0, 0, 1572, 13088]\) | \(143877824/108045\) | \(-322620641280\) | \([2]\) | \(8192\) | \(0.89650\) |
Rank
sage: E.rank()
The elliptic curves in class 10080.q have rank \(1\).
Complex multiplication
The elliptic curves in class 10080.q do not have complex multiplication.Modular form 10080.2.a.q
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
