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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 333795.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333795.o1 | 333795o8 | \([1, 1, 1, -17298204826, -875683873047622]\) | \(23715554832417233918431091521/372220952399189104365\) | \(8984508921781142550658388685\) | \([2]\) | \(566231040\) | \(4.4980\) | |
| 333795.o2 | 333795o6 | \([1, 1, 1, -1113677401, -12815504100202]\) | \(6328611043032432939084721/723183771220991613225\) | \(17455898177526899312639750025\) | \([2, 2]\) | \(283115520\) | \(4.1514\) | |
| 333795.o3 | 333795o4 | \([1, 1, 1, -268027276, 1476321272348]\) | \(88220021994562887162721/12039505273890950625\) | \(290604389274406719186530625\) | \([2, 2]\) | \(141557760\) | \(3.8048\) | |
| 333795.o4 | 333795o2 | \([1, 1, 1, -258546631, 1599994390244]\) | \(79185713292934220826001/1843993463645025\) | \(44509519464280782444225\) | \([2, 2]\) | \(70778880\) | \(3.4583\) | |
| 333795.o5 | 333795o1 | \([1, 1, 1, -258545186, 1600013171198]\) | \(79184385609230668294081/42941745\) | \(1036509332917905\) | \([2]\) | \(35389440\) | \(3.1117\) | \(\Gamma_0(N)\)-optimal |
| 333795.o6 | 333795o3 | \([1, 1, 1, -249089106, 1722465555984]\) | \(-70809965983288820433601/12128017136035299345\) | \(-292740850454234424375592305\) | \([2]\) | \(141557760\) | \(3.8048\) | |
| 333795.o7 | 333795o5 | \([1, 1, 1, 425932529, 7853256712454]\) | \(354040227097633869554159/1308633021594847265625\) | \(-31587219854424115918484765625\) | \([2]\) | \(283115520\) | \(4.1514\) | |
| 333795.o8 | 333795o7 | \([1, 1, 1, 1540448024, -64607045993482]\) | \(16748323164863581359610079/84398855572864120299165\) | \(-2037183199911042231345395829885\) | \([2]\) | \(566231040\) | \(4.4980\) |
Rank
sage: E.rank()
The elliptic curves in class 333795.o have rank \(1\).
Complex multiplication
The elliptic curves in class 333795.o do not have complex multiplication.Modular form 333795.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 8 & 16 & 16 & 8 & 4 \\ 2 & 1 & 2 & 4 & 8 & 8 & 4 & 2 \\ 4 & 2 & 1 & 2 & 4 & 4 & 2 & 4 \\ 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 16 & 8 & 4 & 2 & 1 & 4 & 8 & 16 \\ 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 8 & 4 & 2 & 4 & 8 & 8 & 1 & 8 \\ 4 & 2 & 4 & 8 & 16 & 16 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
