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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 10944.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.bd1 | 10944o3 | \([0, 0, 0, -246540, 47116784]\) | \(8671983378625/82308\) | \(15729303748608\) | \([2]\) | \(55296\) | \(1.6945\) | |
| 10944.bd2 | 10944o4 | \([0, 0, 0, -240780, 49423088]\) | \(-8078253774625/846825858\) | \(-161830941617553408\) | \([2]\) | \(110592\) | \(2.0411\) | |
| 10944.bd3 | 10944o1 | \([0, 0, 0, -4620, -9232]\) | \(57066625/32832\) | \(6274292908032\) | \([2]\) | \(18432\) | \(1.1452\) | \(\Gamma_0(N)\)-optimal |
| 10944.bd4 | 10944o2 | \([0, 0, 0, 18420, -73744]\) | \(3616805375/2105352\) | \(-402339032727552\) | \([2]\) | \(36864\) | \(1.4918\) |
Rank
sage: E.rank()
The elliptic curves in class 10944.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 10944.bd do not have complex multiplication.Modular form 10944.2.a.bd
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
