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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 1584q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1584.o3 | 1584q1 | \([0, 0, 0, -939, -10982]\) | \(30664297/297\) | \(886837248\) | \([2]\) | \(768\) | \(0.53667\) | \(\Gamma_0(N)\)-optimal |
| 1584.o2 | 1584q2 | \([0, 0, 0, -1659, 8170]\) | \(169112377/88209\) | \(263390662656\) | \([2, 2]\) | \(1536\) | \(0.88325\) | |
| 1584.o1 | 1584q3 | \([0, 0, 0, -21099, 1178458]\) | \(347873904937/395307\) | \(1180380377088\) | \([4]\) | \(3072\) | \(1.2298\) | |
| 1584.o4 | 1584q4 | \([0, 0, 0, 6261, 63610]\) | \(9090072503/5845851\) | \(-17455617552384\) | \([2]\) | \(3072\) | \(1.2298\) |
Rank
sage: E.rank()
The elliptic curves in class 1584q have rank \(0\).
Complex multiplication
The elliptic curves in class 1584q do not have complex multiplication.Modular form 1584.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
