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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4800.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.q1 | 4800c5 | \([0, -1, 0, -38433, -2887263]\) | \(3065617154/9\) | \(18432000000\) | \([2]\) | \(8192\) | \(1.1991\) | |
| 4800.q2 | 4800c4 | \([0, -1, 0, -6433, 200737]\) | \(28756228/3\) | \(3072000000\) | \([2]\) | \(4096\) | \(0.85251\) | |
| 4800.q3 | 4800c3 | \([0, -1, 0, -2433, -43263]\) | \(1556068/81\) | \(82944000000\) | \([2, 2]\) | \(4096\) | \(0.85251\) | |
| 4800.q4 | 4800c2 | \([0, -1, 0, -433, 2737]\) | \(35152/9\) | \(2304000000\) | \([2, 2]\) | \(2048\) | \(0.50594\) | |
| 4800.q5 | 4800c1 | \([0, -1, 0, 67, 237]\) | \(2048/3\) | \(-48000000\) | \([2]\) | \(1024\) | \(0.15937\) | \(\Gamma_0(N)\)-optimal |
| 4800.q6 | 4800c6 | \([0, -1, 0, 1567, -175263]\) | \(207646/6561\) | \(-13436928000000\) | \([2]\) | \(8192\) | \(1.1991\) |
Rank
sage: E.rank()
The elliptic curves in class 4800.q have rank \(1\).
Complex multiplication
The elliptic curves in class 4800.q do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
