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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 361920.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.bn1 | 361920bn3 | \([0, -1, 0, -534561, 137908161]\) | \(64443098670429961/6032611833300\) | \(1581412996428595200\) | \([2]\) | \(9437184\) | \(2.2305\) | |
| 361920.bn2 | 361920bn2 | \([0, -1, 0, -118561, -13266239]\) | \(703093388853961/115124490000\) | \(30179194306560000\) | \([2, 2]\) | \(4718592\) | \(1.8839\) | |
| 361920.bn3 | 361920bn1 | \([0, -1, 0, -113441, -14668095]\) | \(615882348586441/21715200\) | \(5692509388800\) | \([2]\) | \(2359296\) | \(1.5373\) | \(\Gamma_0(N)\)-optimal |
| 361920.bn4 | 361920bn4 | \([0, -1, 0, 215519, -74803775]\) | \(4223169036960119/11647532812500\) | \(-3053330841600000000\) | \([2]\) | \(9437184\) | \(2.2305\) |
Rank
sage: E.rank()
The elliptic curves in class 361920.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 361920.bn do not have complex multiplication.Modular form 361920.2.a.bn
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.
