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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 348726o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348726.o6 | 348726o1 | \([1, 0, 1, -3619030062, 615395366299744]\) | \(-111423982835049208609221217/3413049530977153233911808\) | \(-160569922081456964761380083662848\) | \([2]\) | \(1455390720\) | \(4.8601\) | \(\Gamma_0(N)\)-optimal |
| 348726.o5 | 348726o2 | \([1, 0, 1, -132927959342, 18561302360351840]\) | \(5521424264275769466693201984097/31683361580057887676653824\) | \(1490571658575375356747222282098944\) | \([2, 2]\) | \(2910781440\) | \(5.2067\) | |
| 348726.o2 | 348726o3 | \([1, 0, 1, -2123909643262, 1191384900943738400]\) | \(22522169193664496977562630203672417/747984040969628348507664\) | \(35189568181356259898118088131984\) | \([2, 2]\) | \(5821562880\) | \(5.5532\) | |
| 348726.o4 | 348726o4 | \([1, 0, 1, -210889143902, -5723731367983456]\) | \(22047775488403890529761445244257/12458301538998671409274874352\) | \(586111771665848354278848035054144112\) | \([2]\) | \(5821562880\) | \(5.5532\) | |
| 348726.o1 | 348726o5 | \([1, 0, 1, -33982554021322, 76248643432314434384]\) | \(92250802811355064789026667308895058977/101749997212900092\) | \(4786918260628429393121052\) | \([2]\) | \(11643125760\) | \(5.8998\) | |
| 348726.o3 | 348726o6 | \([1, 0, 1, -2120972207922, 1194844642836517936]\) | \(-22428851720936080012736578562556577/129810952265985400081515331068\) | \(-6107070612802229479972360565100730908\) | \([2]\) | \(11643125760\) | \(5.8998\) |
Rank
sage: E.rank()
The elliptic curves in class 348726o have rank \(0\).
Complex multiplication
The elliptic curves in class 348726o do not have complex multiplication.Modular form 348726.2.a.o
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 Cremona numbering.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
