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Properties

Label 17850.bc
Number of curves $2$
Conductor $17850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 17850.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.bc1 17850bd2 \([1, 1, 1, -1351188, 575844531]\) \(17460273607244690041/918397653311250\) \(14349963332988281250\) \([2]\) \(737280\) \(2.4329\)  
17850.bc2 17850bd1 \([1, 1, 1, 55062, 35844531]\) \(1181569139409959/36161310937500\) \(-565020483398437500\) \([2]\) \(368640\) \(2.0863\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17850.bc have rank \(0\).

Complex multiplication

The elliptic curves in class 17850.bc do not have complex multiplication.

Modular form 17850.2.a.bc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.