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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 22080.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22080.bh1 | 22080u4 | \([0, -1, 0, -681185, 216144225]\) | \(133345896593725369/340006815000\) | \(89130746511360000\) | \([4]\) | \(368640\) | \(2.1289\) | |
| 22080.bh2 | 22080u2 | \([0, -1, 0, -59105, 531297]\) | \(87109155423289/49979073600\) | \(13101714269798400\) | \([2, 2]\) | \(184320\) | \(1.7823\) | |
| 22080.bh3 | 22080u1 | \([0, -1, 0, -38625, -2897055]\) | \(24310870577209/114462720\) | \(30005715271680\) | \([2]\) | \(92160\) | \(1.4357\) | \(\Gamma_0(N)\)-optimal |
| 22080.bh4 | 22080u3 | \([0, -1, 0, 235295, 4005217]\) | \(5495662324535111/3207841648920\) | \(-840916441214484480\) | \([2]\) | \(368640\) | \(2.1289\) |
Rank
sage: E.rank()
The elliptic curves in class 22080.bh have rank \(1\).
Complex multiplication
The elliptic curves in class 22080.bh do not have complex multiplication.Modular form 22080.2.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.
