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SageMath
E = EllipticCurve("bp1")
E.isogeny_class()
Elliptic curves in class 116886.bp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116886.bp1 | 116886bo4 | \([1, 0, 0, -183495353, 952067498361]\) | \(385693937170561837203625/2159357734550274048\) | \(3825433947577618042748928\) | \([2]\) | \(31104000\) | \(3.5593\) | |
| 116886.bp2 | 116886bo2 | \([1, 0, 0, -13551458, -18295435740]\) | \(155355156733986861625/8291568305839392\) | \(14689019039461139130912\) | \([2]\) | \(10368000\) | \(3.0100\) | |
| 116886.bp3 | 116886bo3 | \([1, 0, 0, -5073593, 31375532409]\) | \(-8152944444844179625/235342826399858688\) | \(-416924172879760057171968\) | \([2]\) | \(15552000\) | \(3.2127\) | |
| 116886.bp4 | 116886bo1 | \([1, 0, 0, 561982, -1141960764]\) | \(11079872671250375/324440155855872\) | \(-574765526948184456192\) | \([2]\) | \(5184000\) | \(2.6634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116886.bp have rank \(1\).
Complex multiplication
The elliptic curves in class 116886.bp do not have complex multiplication.Modular form 116886.2.a.bp
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
