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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 14994.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 14994.g1 | 14994bi5 | \([1, -1, 0, -6049904373, -181120341567411]\) | \(285531136548675601769470657/17941034271597192\) | \(1538732916202951632332232\) | \([2]\) | \(11796480\) | \(4.1014\) | |
| 14994.g2 | 14994bi3 | \([1, -1, 0, -378838413, -2818625145435]\) | \(70108386184777836280897/552468975892674624\) | \(47383121035157214815613504\) | \([2, 2]\) | \(5898240\) | \(3.7548\) | |
| 14994.g3 | 14994bi6 | \([1, -1, 0, -129038373, -6480344011779]\) | \(-2770540998624539614657/209924951154647363208\) | \(-18004448761648575465228276168\) | \([2]\) | \(11796480\) | \(4.1014\) | |
| 14994.g4 | 14994bi2 | \([1, -1, 0, -40009293, 24490000485]\) | \(82582985847542515777/44772582831427584\) | \(3839970756602740772081664\) | \([2, 2]\) | \(2949120\) | \(3.4082\) | |
| 14994.g5 | 14994bi1 | \([1, -1, 0, -30977613, 66286809189]\) | \(38331145780597164097/55468445663232\) | \(4757313422434680963072\) | \([2]\) | \(1474560\) | \(3.0617\) | \(\Gamma_0(N)\)-optimal |
| 14994.g6 | 14994bi4 | \([1, -1, 0, 154312947, 192501009189]\) | \(4738217997934888496063/2928751705237796928\) | \(-251187673130381225100276288\) | \([2]\) | \(5898240\) | \(3.7548\) |
Rank
sage: E.rank()
The elliptic curves in class 14994.g have rank \(0\).
Complex multiplication
The elliptic curves in class 14994.g do not have complex multiplication.Modular form 14994.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
