Properties

Label 235200.ux
Number of curves $8$
Conductor $235200$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("ux1")
 
E.isogeny_class()
 

Elliptic curves in class 235200.ux

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.ux1 235200ux8 \([0, 1, 0, -27536629633, -1758800397707137]\) \(4791901410190533590281/41160000\) \(19834604912640000000000\) \([2]\) \(254803968\) \(4.3197\)  
235200.ux2 235200ux6 \([0, 1, 0, -1721077633, -27480402827137]\) \(1169975873419524361/108425318400\) \(52249109645072793600000000\) \([2, 2]\) \(127401984\) \(3.9731\)  
235200.ux3 235200ux7 \([0, 1, 0, -1595637633, -31655924107137]\) \(-932348627918877961/358766164249920\) \(-172885935955307880775680000000\) \([2]\) \(254803968\) \(4.3197\)  
235200.ux4 235200ux5 \([0, 1, 0, -341629633, -2387802707137]\) \(9150443179640281/184570312500\) \(88942644000000000000000000\) \([2]\) \(84934656\) \(3.7704\)  
235200.ux5 235200ux3 \([0, 1, 0, -115445633, -362883979137]\) \(353108405631241/86318776320\) \(41596181361752801280000000\) \([2]\) \(63700992\) \(3.6265\)  
235200.ux6 235200ux2 \([0, 1, 0, -45277633, 61546572863]\) \(21302308926361/8930250000\) \(4303400887296000000000000\) \([2, 2]\) \(42467328\) \(3.4238\)  
235200.ux7 235200ux1 \([0, 1, 0, -39005633, 93715660863]\) \(13619385906841/6048000\) \(2914472558592000000000\) \([2]\) \(21233664\) \(3.0772\) \(\Gamma_0(N)\)-optimal
235200.ux8 235200ux4 \([0, 1, 0, 150722367, 452174572863]\) \(785793873833639/637994920500\) \(-307443566190200832000000000\) \([2]\) \(84934656\) \(3.7704\)  

Rank

sage: E.rank()
 

The elliptic curves in class 235200.ux have rank \(2\).

Complex multiplication

The elliptic curves in class 235200.ux do not have complex multiplication.

Modular form 235200.2.a.ux

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - 2 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.