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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 203280.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.bn1 | 203280dh7 | \([0, -1, 0, -12489176, 10692078960]\) | \(29689921233686449/10380965400750\) | \(75327543076118817792000\) | \([2]\) | \(19906560\) | \(3.0911\) | |
| 203280.bn2 | 203280dh4 | \([0, -1, 0, -11153336, 14340618096]\) | \(21145699168383889/2593080\) | \(18816202333716480\) | \([2]\) | \(6635520\) | \(2.5418\) | |
| 203280.bn3 | 203280dh6 | \([0, -1, 0, -5229176, -4478417040]\) | \(2179252305146449/66177562500\) | \(480205163725056000000\) | \([2, 2]\) | \(9953280\) | \(2.7445\) | |
| 203280.bn4 | 203280dh3 | \([0, -1, 0, -5190456, -4549785744]\) | \(2131200347946769/2058000\) | \(14933493915648000\) | \([2]\) | \(4976640\) | \(2.3980\) | |
| 203280.bn5 | 203280dh2 | \([0, -1, 0, -698936, 222996336]\) | \(5203798902289/57153600\) | \(414724459600281600\) | \([2, 2]\) | \(3317760\) | \(2.1952\) | |
| 203280.bn6 | 203280dh5 | \([0, -1, 0, -156856, 559519600]\) | \(-58818484369/18600435000\) | \(-134970594218127360000\) | \([2]\) | \(6635520\) | \(2.5418\) | |
| 203280.bn7 | 203280dh1 | \([0, -1, 0, -79416, -3004560]\) | \(7633736209/3870720\) | \(28087159168696320\) | \([2]\) | \(1658880\) | \(1.8487\) | \(\Gamma_0(N)\)-optimal |
| 203280.bn8 | 203280dh8 | \([0, -1, 0, 1411304, -15081935504]\) | \(42841933504271/13565917968750\) | \(-98438558526000000000000\) | \([2]\) | \(19906560\) | \(3.0911\) |
Rank
sage: E.rank()
The elliptic curves in class 203280.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 203280.bn do not have complex multiplication.Modular form 203280.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
