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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 106470.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106470.bf1 | 106470bt4 | \([1, -1, 0, -503374924935, 85448685505954941]\) | \(4008766897254067912673785886329/1423480510711669921875000000\) | \(5008863165971782207489013671875000000\) | \([2]\) | \(2312110080\) | \(5.7431\) | |
| 106470.bf2 | 106470bt2 | \([1, -1, 0, -212778262215, -36804691187691075]\) | \(302773487204995438715379645049/8911747415025000000000000\) | \(31358155616227096409025000000000000\) | \([2, 2]\) | \(1156055040\) | \(5.3965\) | |
| 106470.bf3 | 106470bt1 | \([1, -1, 0, -211251908295, -37372153247923779]\) | \(296304326013275547793071733369/268420373544960000000\) | \(944502514736617452994560000000\) | \([2]\) | \(578027520\) | \(5.0499\) | \(\Gamma_0(N)\)-optimal |
| 106470.bf4 | 106470bt3 | \([1, -1, 0, 53396737785, -122740514342691075]\) | \(4784981304203817469820354951/1852343836482910078035000000\) | \(-6517923317851044020209679389635000000\) | \([2]\) | \(2312110080\) | \(5.7431\) |
Rank
sage: E.rank()
The elliptic curves in class 106470.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 106470.bf do not have complex multiplication.Modular form 106470.2.a.bf
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.
