Properties

Label 185900bd
Number of curves 4
Conductor 185900
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("185900.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 185900bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185900.bb4 185900bd1 [0, -1, 0, -191533, 31666062] [2] 1866240 \(\Gamma_0(N)\)-optimal
185900.bb3 185900bd2 [0, -1, 0, -423908, -59889688] [2] 3732480  
185900.bb2 185900bd3 [0, -1, 0, -1881533, -980221438] [2] 5598720  
185900.bb1 185900bd4 [0, -1, 0, -29998908, -63232089688] [2] 11197440  

Rank

sage: E.rank()
 

The elliptic curves in class 185900bd have rank \(1\).

Modular form 185900.2.a.bb

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{19} + O(q^{20}) \)

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.