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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 11154.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11154.bg1 | 11154bf3 | \([1, 0, 0, -13608, -609792]\) | \(57736239625/255552\) | \(1233500693568\) | \([2]\) | \(25920\) | \(1.1724\) | |
| 11154.bg2 | 11154bf4 | \([1, 0, 0, -6848, -1214136]\) | \(-7357983625/127552392\) | \(-615671033677128\) | \([2]\) | \(51840\) | \(1.5190\) | |
| 11154.bg3 | 11154bf1 | \([1, 0, 0, -933, 10269]\) | \(18609625/1188\) | \(5734249092\) | \([2]\) | \(8640\) | \(0.62309\) | \(\Gamma_0(N)\)-optimal |
| 11154.bg4 | 11154bf2 | \([1, 0, 0, 757, 43731]\) | \(9938375/176418\) | \(-851535990162\) | \([2]\) | \(17280\) | \(0.96967\) |
Rank
sage: E.rank()
The elliptic curves in class 11154.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 11154.bg do not have complex multiplication.Modular form 11154.2.a.bg
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.
