Properties

Label 5850.bo
Number of curves $6$
Conductor $5850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5850.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5850.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5850.bo1 5850bm5 [1, -1, 1, -2028380, 1112422997] [2] 98304  
5850.bo2 5850bm3 [1, -1, 1, -190130, -31837003] [2] 49152  
5850.bo3 5850bm4 [1, -1, 1, -127130, 17302997] [2, 2] 49152  
5850.bo4 5850bm6 [1, -1, 1, -25880, 44032997] [2] 98304  
5850.bo5 5850bm2 [1, -1, 1, -14630, -247003] [2, 2] 24576  
5850.bo6 5850bm1 [1, -1, 1, 3370, -31003] [2] 12288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5850.bo have rank \(1\).

Modular form 5850.2.a.bo

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.