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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 38640.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38640.bh1 | 38640by4 | \([0, -1, 0, -7717760, 8079048192]\) | \(12411881707829361287041/303132494474220600\) | \(1241630697366407577600\) | \([2]\) | \(2985984\) | \(2.8316\) | |
| 38640.bh2 | 38640by2 | \([0, -1, 0, -949760, -351633408]\) | \(23131609187144855041/322060536000000\) | \(1319159955456000000\) | \([2]\) | \(995328\) | \(2.2823\) | |
| 38640.bh3 | 38640by1 | \([0, -1, 0, -7680, -14745600]\) | \(-12232183057921/22933241856000\) | \(-93934558642176000\) | \([2]\) | \(497664\) | \(1.9358\) | \(\Gamma_0(N)\)-optimal |
| 38640.bh4 | 38640by3 | \([0, -1, 0, 69120, 398069760]\) | \(8915971454369279/16719623332762560\) | \(-68483577170995445760\) | \([2]\) | \(1492992\) | \(2.4851\) |
Rank
sage: E.rank()
The elliptic curves in class 38640.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 38640.bh do not have complex multiplication.Modular form 38640.2.a.bh
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
