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Properties

Label 141610bk
Number of curves $2$
Conductor $141610$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 141610bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141610.cz1 141610bk1 \([1, -1, 1, -38058, -2848163]\) \(-5154200289/20\) \(-23654817620\) \([]\) \(591360\) \(1.2038\) \(\Gamma_0(N)\)-optimal
141610.cz2 141610bk2 \([1, -1, 1, 265392, 27047731]\) \(1747829720511/1280000000\) \(-1513908327680000000\) \([]\) \(4139520\) \(2.1767\)  

Rank

sage: E.rank()
 

The elliptic curves in class 141610bk have rank \(1\).

Complex multiplication

The elliptic curves in class 141610bk do not have complex multiplication.

Modular form 141610.2.a.bk

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.