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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 218530bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 218530.d2 | 218530bc1 | \([1, 1, 0, -54667, 4867821]\) | \(3803721481/26000\) | \(123502710266000\) | \([2]\) | \(1658880\) | \(1.5379\) | \(\Gamma_0(N)\)-optimal |
| 218530.d3 | 218530bc2 | \([1, 1, 0, -21047, 10832009]\) | \(-217081801/10562500\) | \(-50172976045562500\) | \([2]\) | \(3317760\) | \(1.8845\) | |
| 218530.d1 | 218530bc3 | \([1, 1, 0, -348842, -76265644]\) | \(988345570681/44994560\) | \(213728850277928960\) | \([2]\) | \(4976640\) | \(2.0872\) | |
| 218530.d4 | 218530bc4 | \([1, 1, 0, 189078, -289604716]\) | \(157376536199/7722894400\) | \(-36684553442235150400\) | \([2]\) | \(9953280\) | \(2.4338\) |
Rank
sage: E.rank()
The elliptic curves in class 218530bc have rank \(0\).
Complex multiplication
The elliptic curves in class 218530bc do not have complex multiplication.Modular form 218530.2.a.bc
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.
