Properties

Label 324870fb
Number of curves 4
Conductor 324870
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("324870.fb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 324870fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
324870.fb4 324870fb1 [1, 0, 0, 77419, -1399455] [2] 3317760 \(\Gamma_0(N)\)-optimal
324870.fb3 324870fb2 [1, 0, 0, -314581, -11356255] [2, 2] 6635520  
324870.fb2 324870fb3 [1, 0, 0, -3146781, 2137150665] [2] 13271040  
324870.fb1 324870fb4 [1, 0, 0, -3754381, -2795530375] [2] 13271040  

Rank

sage: E.rank()
 

The elliptic curves in class 324870fb have rank \(1\).

Modular form 324870.2.a.fb

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

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.