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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 76230.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.bk1 | 76230i3 | \([1, -1, 0, -114549, 14932385]\) | \(4767078987/6860\) | \(239205697218180\) | \([2]\) | \(414720\) | \(1.6615\) | |
| 76230.bk2 | 76230i4 | \([1, -1, 0, -81879, 23603003]\) | \(-1740992427/5882450\) | \(-205118885364589350\) | \([2]\) | \(829440\) | \(2.0080\) | |
| 76230.bk3 | 76230i1 | \([1, -1, 0, -5649, -141795]\) | \(416832723/56000\) | \(2678600232000\) | \([2]\) | \(138240\) | \(1.1122\) | \(\Gamma_0(N)\)-optimal |
| 76230.bk4 | 76230i2 | \([1, -1, 0, 8871, -760347]\) | \(1613964717/6125000\) | \(-292971900375000\) | \([2]\) | \(276480\) | \(1.4587\) |
Rank
sage: E.rank()
The elliptic curves in class 76230.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 76230.bk do not have complex multiplication.Modular form 76230.2.a.bk
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.
