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Properties

Label 43350.p
Number of curves $8$
Conductor $43350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 43350.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.p1 43350b8 \([1, 1, 0, -819820900, -9035264854250]\) \(161572377633716256481/914742821250\) \(344994811955883457031250\) \([2]\) \(14155776\) \(3.7081\)  
43350.p2 43350b4 \([1, 1, 0, -157216150, 758676014500]\) \(1139466686381936641/4080\) \(1538770023750000\) \([2]\) \(3538944\) \(3.0149\)  
43350.p3 43350b6 \([1, 1, 0, -52164650, -135825948000]\) \(41623544884956481/2962701562500\) \(1117381459238305664062500\) \([2, 2]\) \(7077888\) \(3.3615\)  
43350.p4 43350b3 \([1, 1, 0, -10404150, 10377562500]\) \(330240275458561/67652010000\) \(25514922802557656250000\) \([2, 2]\) \(3538944\) \(3.0149\)  
43350.p5 43350b2 \([1, 1, 0, -9826150, 11850884500]\) \(278202094583041/16646400\) \(6278181696900000000\) \([2, 2]\) \(1769472\) \(2.6683\)  
43350.p6 43350b1 \([1, 1, 0, -578150, 207652500]\) \(-56667352321/16711680\) \(-6302802017280000000\) \([2]\) \(884736\) \(2.3218\) \(\Gamma_0(N)\)-optimal
43350.p7 43350b5 \([1, 1, 0, 22108350, 62300025000]\) \(3168685387909439/6278181696900\) \(-2367813185991575564062500\) \([2]\) \(7077888\) \(3.3615\)  
43350.p8 43350b7 \([1, 1, 0, 47323600, -592576503750]\) \(31077313442863199/420227050781250\) \(-158488428654670715332031250\) \([2]\) \(14155776\) \(3.7081\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43350.p have rank \(1\).

Complex multiplication

The elliptic curves in class 43350.p do not have complex multiplication.

Modular form 43350.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4 q^{11} - q^{12} + 2 q^{13} + q^{16} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.