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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 336a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 336.b4 | 336a1 | \([0, -1, 0, 7, 0]\) | \(2048000/1323\) | \(-21168\) | \([2]\) | \(24\) | \(-0.48107\) | \(\Gamma_0(N)\)-optimal |
| 336.b3 | 336a2 | \([0, -1, 0, -28, 28]\) | \(9826000/5103\) | \(1306368\) | \([2]\) | \(48\) | \(-0.13450\) | |
| 336.b2 | 336a3 | \([0, -1, 0, -113, 516]\) | \(-10061824000/352947\) | \(-5647152\) | \([2]\) | \(72\) | \(0.068235\) | |
| 336.b1 | 336a4 | \([0, -1, 0, -1828, 30700]\) | \(2640279346000/3087\) | \(790272\) | \([2]\) | \(144\) | \(0.41481\) |
Rank
sage: E.rank()
The elliptic curves in class 336a have rank \(0\).
Complex multiplication
The elliptic curves in class 336a do not have complex multiplication.Modular form 336.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
