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SageMath
E = EllipticCurve("eo1")
E.isogeny_class()
Elliptic curves in class 200970.eo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200970.eo1 | 200970g8 | \([1, -1, 1, -6058939262, 123339176340149]\) | \(33743177813840232088099335886489/10512677519144598197082375000\) | \(7663741911456412085673051375000\) | \([6]\) | \(467140608\) | \(4.6305\) | |
| 200970.eo2 | 200970g6 | \([1, -1, 1, -5502064262, 157063080840149]\) | \(25268133291250118646200025886489/4463489141983265625000000\) | \(3253883584505800640625000000\) | \([2, 6]\) | \(233570304\) | \(4.2840\) | |
| 200970.eo3 | 200970g3 | \([1, -1, 1, -5501830982, 157077067002581]\) | \(25264919424633968163234466954009/788559976512000000\) | \(574860222877248000000\) | \([6]\) | \(116785152\) | \(3.9374\) | |
| 200970.eo4 | 200970g7 | \([1, -1, 1, -4948921742, 189891868145141]\) | \(-18387722572391758931230103324569/10726928227901458740234375000\) | \(-7819930678140163421630859375000\) | \([6]\) | \(467140608\) | \(4.6305\) | |
| 200970.eo5 | 200970g5 | \([1, -1, 1, -2347269377, -43761866250949]\) | \(1961936660078092398490361110729/474945809169127845190950\) | \(346235494884294199144202550\) | \([2]\) | \(155713536\) | \(4.0812\) | |
| 200970.eo6 | 200970g2 | \([1, -1, 1, -164096627, -511467535249]\) | \(670340013887004175017226729/232881726498686518522500\) | \(169770778617542472002902500\) | \([2, 2]\) | \(77856768\) | \(3.7346\) | |
| 200970.eo7 | 200970g1 | \([1, -1, 1, -68437247, 212061751319]\) | \(48626585041073592629153449/1495685481508052326800\) | \(1090354716019370146237200\) | \([2]\) | \(38928384\) | \(3.3881\) | \(\Gamma_0(N)\)-optimal |
| 200970.eo8 | 200970g4 | \([1, -1, 1, 488526043, -3568091072461]\) | \(17687210581982180689098502391/17779596413363063064843750\) | \(-12961325785341672974271093750\) | \([2]\) | \(155713536\) | \(4.0812\) |
Rank
sage: E.rank()
The elliptic curves in class 200970.eo have rank \(0\).
Complex multiplication
The elliptic curves in class 200970.eo do not have complex multiplication.Modular form 200970.2.a.eo
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 3 & 6 & 12 & 12 \\ 2 & 1 & 2 & 2 & 6 & 3 & 6 & 6 \\ 4 & 2 & 1 & 4 & 12 & 6 & 3 & 12 \\ 4 & 2 & 4 & 1 & 12 & 6 & 12 & 3 \\ 3 & 6 & 12 & 12 & 1 & 2 & 4 & 4 \\ 6 & 3 & 6 & 6 & 2 & 1 & 2 & 2 \\ 12 & 6 & 3 & 12 & 4 & 2 & 1 & 4 \\ 12 & 6 & 12 & 3 & 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
