Properties

Label 4830bk
Number of curves $4$
Conductor $4830$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4830bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.bk3 4830bk1 \([1, 0, 0, -480, 230400]\) \(-12232183057921/22933241856000\) \(-22933241856000\) \([6]\) \(20736\) \(1.2426\) \(\Gamma_0(N)\)-optimal
4830.bk2 4830bk2 \([1, 0, 0, -59360, 5494272]\) \(23131609187144855041/322060536000000\) \(322060536000000\) \([6]\) \(41472\) \(1.5892\)  
4830.bk4 4830bk3 \([1, 0, 0, 4320, -6219840]\) \(8915971454369279/16719623332762560\) \(-16719623332762560\) \([2]\) \(62208\) \(1.7919\)  
4830.bk1 4830bk4 \([1, 0, 0, -482360, -126235128]\) \(12411881707829361287041/303132494474220600\) \(303132494474220600\) \([2]\) \(124416\) \(2.1385\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4830bk have rank \(1\).

Complex multiplication

The elliptic curves in class 4830bk do not have complex multiplication.

Modular form 4830.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 6q^{11} + q^{12} - 4q^{13} + q^{14} + q^{15} + q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.