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Properties

Label 174570.a
Number of curves $4$
Conductor $174570$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 174570.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174570.a1 174570cp4 \([1, 1, 0, -186886453, -983443097363]\) \(4876297165069215549481/969819840\) \(143568142184237760\) \([2]\) \(32440320\) \(3.1225\)  
174570.a2 174570cp2 \([1, 1, 0, -11681653, -15366495443]\) \(1190884543636720681/530916249600\) \(78594658994081894400\) \([2, 2]\) \(16220160\) \(2.7759\)  
174570.a3 174570cp3 \([1, 1, 0, -9819573, -20427256467]\) \(-707350352645673001/807856192440000\) \(-119591709632010479160000\) \([2]\) \(32440320\) \(3.1225\)  
174570.a4 174570cp1 \([1, 1, 0, -847733, -157838547]\) \(455129268177961/191008604160\) \(28276128523474698240\) \([2]\) \(8110080\) \(2.4293\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 174570.a have rank \(0\).

Complex multiplication

The elliptic curves in class 174570.a do not have complex multiplication.

Modular form 174570.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 2 q^{13} + 4 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.