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Properties

Label 380926.bk
Number of curves $2$
Conductor $380926$
CM no
Rank $1$
Graph

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

Elliptic curves in class 380926.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
380926.bk1 380926bk2 \([1, 1, 1, -164953552, 590774482605]\) \(2154177617137/592143556\) \(136443931920811938347685124\) \([]\) \(171714816\) \(3.7224\)  
380926.bk2 380926bk1 \([1, 1, 1, -59453612, -176421081075]\) \(100862848177/33856\) \(7801226091719908853824\) \([]\) \(57238272\) \(3.1731\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 380926.bk have rank \(1\).

Complex multiplication

The elliptic curves in class 380926.bk do not have complex multiplication.

Modular form 380926.2.a.bk

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.