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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 338130.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338130.y1 | 338130y7 | \([1, -1, 0, -17143191015660, 27320313468836296300]\) | \(31664865542564944883878115208137569/103216295812500\) | \(1816223646869901133312500\) | \([2]\) | \(7644119040\) | \(5.7401\) | |
| 338130.y2 | 338130y6 | \([1, -1, 0, -1071449453160, 426880086563858800]\) | \(7730680381889320597382223137569/441370202660156250000\) | \(7766477112793805170628906250000\) | \([2, 2]\) | \(3822059520\) | \(5.3935\) | |
| 338130.y3 | 338130y8 | \([1, -1, 0, -1069506558180, 428505349689527476]\) | \(-7688701694683937879808871873249/58423707246780395507812500\) | \(-1028040367115717170000076293945312500\) | \([2]\) | \(7644119040\) | \(5.7401\) | |
| 338130.y4 | 338130y4 | \([1, -1, 0, -211651864920, 37473670967754496]\) | \(59589391972023341137821784609/8834417507562311995200\) | \(155452953017259535808493730555200\) | \([2]\) | \(2548039680\) | \(5.1908\) | |
| 338130.y5 | 338130y3 | \([1, -1, 0, -67087036440, 6644606911560256]\) | \(1897660325010178513043539489/14258428094958372000000\) | \(250895404348751670826419972000000\) | \([2]\) | \(1911029760\) | \(5.0470\) | |
| 338130.y6 | 338130y2 | \([1, -1, 0, -14454448920, 470482963468096]\) | \(18980483520595353274840609/5549773448629762560000\) | \(97655410832437591100054530560000\) | \([2, 2]\) | \(1274019840\) | \(4.8442\) | |
| 338130.y7 | 338130y1 | \([1, -1, 0, -5452075800, -149202592145600]\) | \(1018563973439611524445729/42904970360310988800\) | \(754968206553406826787687628800\) | \([2]\) | \(637009920\) | \(4.4977\) | \(\Gamma_0(N)\)-optimal |
| 338130.y8 | 338130y5 | \([1, -1, 0, 38704997160, 3127062489980800]\) | \(364421318680576777174674911/450962301637624725000000\) | \(-7935262447017018271133479725000000\) | \([2]\) | \(2548039680\) | \(5.1908\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.y have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.y do not have complex multiplication.Modular form 338130.2.a.y
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
