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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 142800.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.ct1 | 142800dm5 | \([0, -1, 0, -5487441608, 156461696585712]\) | \(285531136548675601769470657/17941034271597192\) | \(1148226193382220288000000\) | \([2]\) | \(94371840\) | \(4.0770\) | |
| 142800.ct2 | 142800dm3 | \([0, -1, 0, -343617608, 2435030729712]\) | \(70108386184777836280897/552468975892674624\) | \(35358014457131175936000000\) | \([2, 2]\) | \(47185920\) | \(3.7304\) | |
| 142800.ct3 | 142800dm6 | \([0, -1, 0, -117041608, 5598031689712]\) | \(-2770540998624539614657/209924951154647363208\) | \(-13435196873897431245312000000\) | \([2]\) | \(94371840\) | \(4.0770\) | |
| 142800.ct4 | 142800dm2 | \([0, -1, 0, -36289608, -21134646288]\) | \(82582985847542515777/44772582831427584\) | \(2865445301211365376000000\) | \([2, 2]\) | \(23592960\) | \(3.3838\) | |
| 142800.ct5 | 142800dm1 | \([0, -1, 0, -28097608, -57244982288]\) | \(38331145780597164097/55468445663232\) | \(3549980522446848000000\) | \([2]\) | \(11796480\) | \(3.0373\) | \(\Gamma_0(N)\)-optimal |
| 142800.ct6 | 142800dm4 | \([0, -1, 0, 139966392, -166369590288]\) | \(4738217997934888496063/2928751705237796928\) | \(-187440109135219003392000000\) | \([2]\) | \(47185920\) | \(3.7304\) |
Rank
sage: E.rank()
The elliptic curves in class 142800.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 142800.ct do not have complex multiplication.Modular form 142800.2.a.ct
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.
