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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 338130.bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.bb1 | 338130bb4 | \([1, -1, 0, -199288674, -1080965915172]\) | \(49745123032831462081/97939634471640\) | \(1723373995287718012463640\) | \([2]\) | \(106168320\) | \(3.5386\) | |
| 338130.bb2 | 338130bb3 | \([1, -1, 0, -167036274, 826659712908]\) | \(29291056630578924481/175463302795560\) | \(3087502774504681624963560\) | \([2]\) | \(106168320\) | \(3.5386\) | |
| 338130.bb3 | 338130bb2 | \([1, -1, 0, -16698474, -4377577932]\) | \(29263955267177281/16463793153600\) | \(289701642626878999233600\) | \([2, 2]\) | \(53084160\) | \(3.1920\) | |
| 338130.bb4 | 338130bb1 | \([1, -1, 0, 4109526, -544744332]\) | \(436192097814719/259683840000\) | \(-4569471585908835840000\) | \([2]\) | \(26542080\) | \(2.8455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 338130.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 338130.bb do not have complex multiplication.Modular form 338130.2.a.bb
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
