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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 57798.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57798.bm1 | 57798bf3 | \([1, -1, 1, -651020, 202341611]\) | \(8671983378625/82308\) | \(289620761480388\) | \([2]\) | \(622080\) | \(1.9373\) | |
| 57798.bm2 | 57798bf4 | \([1, -1, 1, -635810, 212234195]\) | \(-8078253774625/846825858\) | \(-2979763204490971938\) | \([2]\) | \(1244160\) | \(2.2839\) | |
| 57798.bm3 | 57798bf1 | \([1, -1, 1, -12200, -36565]\) | \(57066625/32832\) | \(115527395161152\) | \([2]\) | \(207360\) | \(1.3880\) | \(\Gamma_0(N)\)-optimal |
| 57798.bm4 | 57798bf2 | \([1, -1, 1, 48640, -328597]\) | \(3616805375/2105352\) | \(-7408194214708872\) | \([2]\) | \(414720\) | \(1.7346\) |
Rank
sage: E.rank()
The elliptic curves in class 57798.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 57798.bm do not have complex multiplication.Modular form 57798.2.a.bm
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
