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SageMath
E = EllipticCurve("lx1")
E.isogeny_class()
Elliptic curves in class 374850lx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 374850.lx7 | 374850lx1 | \([1, -1, 1, -356394380, 3086865871247]\) | \(-3735772816268612449/909650165760000\) | \(-1219018221628784640000000000\) | \([2]\) | \(169869312\) | \(3.9157\) | \(\Gamma_0(N)\)-optimal |
| 374850.lx6 | 374850lx2 | \([1, -1, 1, -6001194380, 178933675471247]\) | \(17836145204788591940449/770635366502400\) | \(1032725095161315393600000000\) | \([2, 2]\) | \(339738624\) | \(4.2623\) | |
| 374850.lx8 | 374850lx3 | \([1, -1, 1, 2564789620, -20999947312753]\) | \(1392333139184610040991/947901937500000000\) | \(-1270279254183741210937500000000\) | \([2]\) | \(509607936\) | \(4.4650\) | |
| 374850.lx3 | 374850lx4 | \([1, -1, 1, -96018114380, 11451932600911247]\) | \(73054578035931991395831649/136386452160\) | \(182770889979926115000000\) | \([2]\) | \(679477248\) | \(4.6089\) | |
| 374850.lx5 | 374850lx5 | \([1, -1, 1, -6301074380, 160062826831247]\) | \(20645800966247918737249/3688936444974392640\) | \(4943527648452868766621085000000\) | \([2]\) | \(679477248\) | \(4.6089\) | |
| 374850.lx4 | 374850lx6 | \([1, -1, 1, -11216460380, -175129447312753]\) | \(116454264690812369959009/57505157319440250000\) | \(77062410637236689590160156250000\) | \([2, 2]\) | \(1019215872\) | \(4.8116\) | |
| 374850.lx2 | 374850lx7 | \([1, -1, 1, -96301897880, 11380834332187247]\) | \(73704237235978088924479009/899277423164136103500\) | \(1205117754494742186144523804687500\) | \([2]\) | \(2038431744\) | \(5.1582\) | |
| 374850.lx1 | 374850lx8 | \([1, -1, 1, -146631022880, -21595546601812753]\) | \(260174968233082037895439009/223081361502731896500\) | \(298950360054500713527788695312500\) | \([2]\) | \(2038431744\) | \(5.1582\) |
Rank
sage: E.rank()
The elliptic curves in class 374850lx have rank \(1\).
Complex multiplication
The elliptic curves in class 374850lx do not have complex multiplication.Modular form 374850.2.a.lx
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.
