Properties

Label 201810.p
Number of curves $8$
Conductor $201810$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 201810.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
201810.p1 201810cg7 \([1, 1, 0, -337534452, 2386710180624]\) \(4791901410190533590281/41160000\) \(36529651509960000\) \([2]\) \(34836480\) \(3.2193\)  
201810.p2 201810cg6 \([1, 1, 0, -21096372, 37284011856]\) \(1169975873419524361/108425318400\) \(96227869193597030400\) \([2, 2]\) \(17418240\) \(2.8727\)  
201810.p3 201810cg8 \([1, 1, 0, -19558772, 42951297936]\) \(-932348627918877961/358766164249920\) \(-318406291390054603955520\) \([2]\) \(34836480\) \(3.2193\)  
201810.p4 201810cg4 \([1, 1, 0, -4187577, 3238581249]\) \(9150443179640281/184570312500\) \(163806831747070312500\) \([2]\) \(11612160\) \(2.6700\)  
201810.p5 201810cg3 \([1, 1, 0, -1415092, 491827024]\) \(353108405631241/86318776320\) \(76608231723415633920\) \([2]\) \(8709120\) \(2.5261\)  
201810.p6 201810cg2 \([1, 1, 0, -554997, -83776419]\) \(21302308926361/8930250000\) \(7925629747250250000\) \([2, 2]\) \(5806080\) \(2.3234\)  
201810.p7 201810cg1 \([1, 1, 0, -478117, -127398131]\) \(13619385906841/6048000\) \(5367622262688000\) \([2]\) \(2903040\) \(1.9768\) \(\Gamma_0(N)\)-optimal
201810.p8 201810cg5 \([1, 1, 0, 1847503, -612806919]\) \(785793873833639/637994920500\) \(-566222840403052360500\) \([2]\) \(11612160\) \(2.6700\)  

Rank

sage: E.rank()
 

The elliptic curves in class 201810.p have rank \(0\).

Complex multiplication

The elliptic curves in class 201810.p do not have complex multiplication.

Modular form 201810.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - 2 q^{13} - q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.