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Properties

Label 174570.b
Number of curves $2$
Conductor $174570$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 174570.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
174570.b1 174570co1 \([1, 1, 0, -19235773, -15531975107]\) \(437020845889103/195104194560\) \(351412439294338966241280\) \([2]\) \(33384960\) \(3.2135\) \(\Gamma_0(N)\)-optimal
174570.b2 174570co2 \([1, 1, 0, 66419907, -115937563203]\) \(17991524611989937/13637201212800\) \(-24562681259341171422326400\) \([2]\) \(66769920\) \(3.5601\)  

Rank

sage: E.rank()
 

The elliptic curves in class 174570.b have rank \(1\).

Complex multiplication

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

Modular form 174570.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.