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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 22080.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22080.bg1 | 22080ch4 | \([0, -1, 0, -4225, -102623]\) | \(63649751618/1164375\) | \(152616960000\) | \([2]\) | \(24576\) | \(0.94080\) | |
| 22080.bg2 | 22080ch2 | \([0, -1, 0, -545, 2625]\) | \(273671716/119025\) | \(7800422400\) | \([2, 2]\) | \(12288\) | \(0.59423\) | |
| 22080.bg3 | 22080ch1 | \([0, -1, 0, -465, 4017]\) | \(680136784/345\) | \(5652480\) | \([2]\) | \(6144\) | \(0.24766\) | \(\Gamma_0(N)\)-optimal |
| 22080.bg4 | 22080ch3 | \([0, -1, 0, 1855, 17505]\) | \(5382838942/4197615\) | \(-550189793280\) | \([4]\) | \(24576\) | \(0.94080\) |
Rank
sage: E.rank()
The elliptic curves in class 22080.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 22080.bg do not have complex multiplication.Modular form 22080.2.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.
