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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 361920.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 361920.b1 | 361920b3 | \([0, -1, 0, -278021, -55772379]\) | \(2320909044001816576/26487235057725\) | \(27122928699110400\) | \([2]\) | \(3317760\) | \(1.9664\) | |
| 361920.b2 | 361920b4 | \([0, -1, 0, -58321, -141762959]\) | \(-1339017045088336/529264868675985\) | \(-8671475608387338240\) | \([2]\) | \(6635520\) | \(2.3130\) | |
| 361920.b3 | 361920b1 | \([0, -1, 0, -26021, 1582821]\) | \(1902884346904576/55825453125\) | \(57165264000000\) | \([2]\) | \(1105920\) | \(1.4171\) | \(\Gamma_0(N)\)-optimal |
| 361920.b4 | 361920b2 | \([0, -1, 0, 6479, 5242321]\) | \(1835526588464/726280556625\) | \(-11899380639744000\) | \([2]\) | \(2211840\) | \(1.7637\) |
Rank
sage: E.rank()
The elliptic curves in class 361920.b have rank \(2\).
Complex multiplication
The elliptic curves in class 361920.b do not have complex multiplication.Modular form 361920.2.a.b
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.
