Properties

Label 303240bp
Number of curves $6$
Conductor $303240$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("303240.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303240bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303240.bp4 303240bp1 [0, 1, 0, -63295, -6150250] [2] 884736 \(\Gamma_0(N)\)-optimal
303240.bp3 303240bp2 [0, 1, 0, -65100, -5782752] [2, 2] 1769472  
303240.bp2 303240bp3 [0, 1, 0, -245600, 40569648] [2, 2] 3538944  
303240.bp5 303240bp4 [0, 1, 0, 86520, -28586400] [2] 3538944  
303240.bp1 303240bp5 [0, 1, 0, -3783400, 2831186288] [2] 7077888  
303240.bp6 303240bp6 [0, 1, 0, 404200, 219394608] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 303240bp have rank \(0\).

Modular form 303240.2.a.bp

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} - 4q^{11} + 2q^{13} + q^{15} + 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.