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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 24990bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24990.bq7 | 24990bs1 | \([1, 1, 1, -1583975, -915260515]\) | \(-3735772816268612449/909650165760000\) | \(-107019432351498240000\) | \([4]\) | \(884736\) | \(2.5617\) | \(\Gamma_0(N)\)-optimal |
| 24990.bq6 | 24990bs2 | \([1, 1, 1, -26671975, -53028054115]\) | \(17836145204788591940449/770635366502400\) | \(90664480233640857600\) | \([2, 2]\) | \(1769472\) | \(2.9083\) | |
| 24990.bq8 | 24990bs3 | \([1, 1, 1, 11399065, 6226766237]\) | \(1392333139184610040991/947901937500000000\) | \(-111519715044937500000000\) | \([4]\) | \(2654208\) | \(3.1110\) | |
| 24990.bq5 | 24990bs4 | \([1, 1, 1, -28004775, -47437224675]\) | \(20645800966247918737249/3688936444974392640\) | \(433999683814792319703360\) | \([2]\) | \(3538944\) | \(3.2549\) | |
| 24990.bq3 | 24990bs5 | \([1, 1, 1, -426747175, -3393335913955]\) | \(73054578035931991395831649/136386452160\) | \(16045729710171840\) | \([2]\) | \(3538944\) | \(3.2549\) | |
| 24990.bq4 | 24990bs6 | \([1, 1, 1, -49850935, 51870266237]\) | \(116454264690812369959009/57505157319440250000\) | \(6765424253474825972250000\) | \([2, 2]\) | \(5308416\) | \(3.4576\) | |
| 24990.bq1 | 24990bs7 | \([1, 1, 1, -651693435, 6398419797237]\) | \(260174968233082037895439009/223081361502731896500\) | \(26245299099434904891328500\) | \([2]\) | \(10616832\) | \(3.8042\) | |
| 24990.bq2 | 24990bs8 | \([1, 1, 1, -428008435, -3372270264763]\) | \(73704237235978088924479009/899277423164136103500\) | \(105799089557837448440671500\) | \([2]\) | \(10616832\) | \(3.8042\) |
Rank
sage: E.rank()
The elliptic curves in class 24990bs have rank \(1\).
Complex multiplication
The elliptic curves in class 24990bs do not have complex multiplication.Modular form 24990.2.a.bs
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
