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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 133518.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 133518.bo1 | 133518bx3 | \([1, 0, 1, -19809945, 33935314168]\) | \(35618855581745079337/188166132\) | \(4541872994613108\) | \([2]\) | \(5308416\) | \(2.6209\) | |
| 133518.bo2 | 133518bx2 | \([1, 0, 1, -1238805, 529547536]\) | \(8710408612492777/19986042384\) | \(482414477080724496\) | \([2, 2]\) | \(2654208\) | \(2.2743\) | |
| 133518.bo3 | 133518bx4 | \([1, 0, 1, -793745, 915325544]\) | \(-2291249615386537/13671036998388\) | \(-329985598850143238772\) | \([2]\) | \(5308416\) | \(2.6209\) | |
| 133518.bo4 | 133518bx1 | \([1, 0, 1, -105925, 1625456]\) | \(5445273626857/3103398144\) | \(74908486835271936\) | \([2]\) | \(1327104\) | \(1.9277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 133518.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 133518.bo do not have complex multiplication.Modular form 133518.2.a.bo
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.
