Properties

Label 279312bp
Number of curves 4
Conductor 279312
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("279312.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 279312bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
279312.bp4 279312bp1 [0, -1, 0, 353, 69730] [2] 608256 \(\Gamma_0(N)\)-optimal
279312.bp3 279312bp2 [0, -1, 0, -23452, 1355200] [2, 2] 1216512  
279312.bp1 279312bp3 [0, -1, 0, -372592, 87662608] [2] 2433024  
279312.bp2 279312bp4 [0, -1, 0, -55192, -3063008] [2] 2433024  

Rank

sage: E.rank()
 

The elliptic curves in class 279312bp have rank \(0\).

Modular form 279312.2.a.bp

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.