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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 5610.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5610.bh1 | 5610bi3 | \([1, 0, 0, -19971, -1059399]\) | \(880895732965860529/26454814115400\) | \(26454814115400\) | \([2]\) | \(18432\) | \(1.3521\) | |
| 5610.bh2 | 5610bi2 | \([1, 0, 0, -2971, 38801]\) | \(2900285849172529/1019696040000\) | \(1019696040000\) | \([2, 2]\) | \(9216\) | \(1.0055\) | |
| 5610.bh3 | 5610bi1 | \([1, 0, 0, -2651, 52305]\) | \(2060455000819249/517017600\) | \(517017600\) | \([2]\) | \(4608\) | \(0.65894\) | \(\Gamma_0(N)\)-optimal |
| 5610.bh4 | 5610bi4 | \([1, 0, 0, 8909, 274025]\) | \(78200142092480591/77517928125000\) | \(-77517928125000\) | \([2]\) | \(18432\) | \(1.3521\) |
Rank
sage: E.rank()
The elliptic curves in class 5610.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 5610.bh do not have complex multiplication.Modular form 5610.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
