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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 38808.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38808.q1 | 38808bh4 | \([0, 0, 0, -110691, 13984110]\) | \(1707831108/26411\) | \(2319533078252544\) | \([2]\) | \(196608\) | \(1.7496\) | |
| 38808.q2 | 38808bh2 | \([0, 0, 0, -13671, -277830]\) | \(12869712/5929\) | \(130177876840704\) | \([2, 2]\) | \(98304\) | \(1.4031\) | |
| 38808.q3 | 38808bh1 | \([0, 0, 0, -11466, -472311]\) | \(121485312/77\) | \(105663861072\) | \([2]\) | \(49152\) | \(1.0565\) | \(\Gamma_0(N)\)-optimal |
| 38808.q4 | 38808bh3 | \([0, 0, 0, 48069, -2092986]\) | \(139863132/102487\) | \(-9000870341557248\) | \([2]\) | \(196608\) | \(1.7496\) |
Rank
sage: E.rank()
The elliptic curves in class 38808.q have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.q do not have complex multiplication.Modular form 38808.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
