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Properties

Label 185150.bk
Number of curves $2$
Conductor $185150$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 185150.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185150.bk1 185150f2 \([1, 0, 0, -8008013, -8166591983]\) \(24553362849625/1755162752\) \(4059798098937602000000\) \([2]\) \(17031168\) \(2.8932\)  
185150.bk2 185150f1 \([1, 0, 0, 455987, -557455983]\) \(4533086375/60669952\) \(-140333285623552000000\) \([2]\) \(8515584\) \(2.5466\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 185150.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 185150.bk do not have complex multiplication.

Modular form 185150.2.a.bk

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