Properties

Label 43350cy
Number of curves $4$
Conductor $43350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cy1")
 
E.isogeny_class()
 

Elliptic curves in class 43350cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.dl2 43350cy1 \([1, 0, 0, -1846138, 964969892]\) \(1845026709625/793152\) \(299136892617000000\) \([2]\) \(995328\) \(2.3134\) \(\Gamma_0(N)\)-optimal
43350.dl3 43350cy2 \([1, 0, 0, -1557138, 1277378892]\) \(-1107111813625/1228691592\) \(-463400438775310125000\) \([2]\) \(1990656\) \(2.6600\)  
43350.dl1 43350cy3 \([1, 0, 0, -5422513, -3674888983]\) \(46753267515625/11591221248\) \(4371623479185408000000\) \([2]\) \(2985984\) \(2.8628\)  
43350.dl4 43350cy4 \([1, 0, 0, 13073487, -23299144983]\) \(655215969476375/1001033261568\) \(-377539209724885128000000\) \([2]\) \(5971968\) \(3.2093\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 43350.2.a.cy

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.