Show commands:
SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 334950.gb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334950.gb1 | 334950gb3 | \([1, 0, 0, -89537553, -95269046103]\) | \(635081355617346114324952229/336161529228687156707328\) | \(42020191153585894588416000\) | \([10]\) | \(118400000\) | \(3.6082\) | |
| 334950.gb2 | 334950gb1 | \([1, 0, 0, -70507028, -227880899328]\) | \(310106540269005530552722709/530664446928\) | \(66333055866000\) | \([2]\) | \(23680000\) | \(2.8035\) | \(\Gamma_0(N)\)-optimal |
| 334950.gb3 | 334950gb2 | \([1, 0, 0, -70506328, -227885650228]\) | \(-310097304065360879030769749/12828204957789728892\) | \(-1603525619723716111500\) | \([2]\) | \(47360000\) | \(3.1500\) | |
| 334950.gb4 | 334950gb4 | \([1, 0, 0, 340721647, -744530178903]\) | \(34995554416298589943122512731/22167950922230373214682112\) | \(-2770993865278796651835264000\) | \([10]\) | \(236800000\) | \(3.9548\) |
Rank
sage: E.rank()
The elliptic curves in class 334950.gb have rank \(0\).
Complex multiplication
The elliptic curves in class 334950.gb do not have complex multiplication.Modular form 334950.2.a.gb
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
