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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 249090n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 249090.n4 | 249090n1 | \([1, 1, 0, -36635298027, 2748750571788669]\) | \(-115584950942853977541113570881/2491093505441506976133120\) | \(-117195688616873989659828603678720\) | \([2]\) | \(1625702400\) | \(4.9433\) | \(\Gamma_0(N)\)-optimal |
| 249090.n3 | 249090n2 | \([1, 1, 0, -589163876907, 174061009993543101]\) | \(480740200620847978249776918657601/216345287040017637326400\) | \(10178154628995512003558972558400\) | \([2, 2]\) | \(3251404800\) | \(5.2898\) | |
| 249090.n1 | 249090n3 | \([1, 1, 0, -9426621012387, 11139918949542556629]\) | \(1969111223714702304368067230802256321/398790253238535000\) | \(18761438797819982224335000\) | \([2]\) | \(6502809600\) | \(5.6364\) | |
| 249090.n2 | 249090n4 | \([1, 1, 0, -592164003507, 172198724008390821]\) | \(488121703486772881794230641464001/10193134424111701474411057320\) | \(479544989133762638272667147760898920\) | \([2]\) | \(6502809600\) | \(5.6364\) |
Rank
sage: E.rank()
The elliptic curves in class 249090n have rank \(0\).
Complex multiplication
The elliptic curves in class 249090n do not have complex multiplication.Modular form 249090.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
