Properties

Label 4410.bk
Number of curves $2$
Conductor $4410$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4410.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.bk1 4410x2 \([1, -1, 1, -791237, 271095661]\) \(68971442301/400\) \(317712018632400\) \([2]\) \(43008\) \(1.9729\)  
4410.bk2 4410x1 \([1, -1, 1, -50357, 4082509]\) \(17779581/1280\) \(1016678459623680\) \([2]\) \(21504\) \(1.6263\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4410.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 4410.bk do not have complex multiplication.

Modular form 4410.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 2q^{11} + 2q^{13} + q^{16} + 2q^{17} + 6q^{19} + O(q^{20})\)  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.