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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 22848.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.bg1 | 22848r4 | \([0, -1, 0, -2177, -34815]\) | \(17418812548/1753941\) | \(114946277376\) | \([2]\) | \(20480\) | \(0.85845\) | |
| 22848.bg2 | 22848r2 | \([0, -1, 0, -497, 3825]\) | \(830321872/127449\) | \(2088124416\) | \([2, 2]\) | \(10240\) | \(0.51187\) | |
| 22848.bg3 | 22848r1 | \([0, -1, 0, -477, 4173]\) | \(11745974272/357\) | \(365568\) | \([2]\) | \(5120\) | \(0.16530\) | \(\Gamma_0(N)\)-optimal |
| 22848.bg4 | 22848r3 | \([0, -1, 0, 863, 19873]\) | \(1083360092/3306177\) | \(-216673615872\) | \([2]\) | \(20480\) | \(0.85845\) |
Rank
sage: E.rank()
The elliptic curves in class 22848.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 22848.bg do not have complex multiplication.Modular form 22848.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
