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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 369600.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.b1 | 369600b3 | \([0, -1, 0, -19493633, 32986555137]\) | \(200005594092187129/1027287538200\) | \(4207769756467200000000\) | \([2]\) | \(28311552\) | \(2.9952\) | |
| 369600.b2 | 369600b2 | \([0, -1, 0, -1893633, -119044863]\) | \(183337554283129/104587560000\) | \(428390645760000000000\) | \([2, 2]\) | \(14155776\) | \(2.6487\) | |
| 369600.b3 | 369600b1 | \([0, -1, 0, -1381633, -623364863]\) | \(71210194441849/165580800\) | \(678218956800000000\) | \([2]\) | \(7077888\) | \(2.3021\) | \(\Gamma_0(N)\)-optimal |
| 369600.b4 | 369600b4 | \([0, -1, 0, 7514367, -956356863]\) | \(11456208593737991/6725709375000\) | \(-27548505600000000000000\) | \([2]\) | \(28311552\) | \(2.9952\) |
Rank
sage: E.rank()
The elliptic curves in class 369600.b have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.b do not have complex multiplication.Modular form 369600.2.a.b
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.
