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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 440440.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 440440.bn1 | 440440bn1 | \([0, 0, 0, -332387, 3654926]\) | \(2238719766084/1292374265\) | \(2344468321564328960\) | \([2]\) | \(4838400\) | \(2.2144\) | \(\Gamma_0(N)\)-optimal |
| 440440.bn2 | 440440bn2 | \([0, 0, 0, 1327733, 29220774]\) | \(71346044015118/41389887175\) | \(-150169005903114598400\) | \([2]\) | \(9676800\) | \(2.5610\) |
Rank
sage: E.rank()
The elliptic curves in class 440440.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 440440.bn do not have complex multiplication.Modular form 440440.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
