Properties

Label 34914o
Number of curves 4
Conductor 34914
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("34914.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 34914o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34914.o3 34914o1 [1, 0, 1, -2921, -57544] [2] 47520 \(\Gamma_0(N)\)-optimal
34914.o4 34914o2 [1, 0, 1, 2369, -241636] [2] 95040  
34914.o1 34914o3 [1, 0, 1, -42596, 3367202] [2] 142560  
34914.o2 34914o4 [1, 0, 1, -21436, 6718946] [2] 285120  

Rank

sage: E.rank()
 

The elliptic curves in class 34914o have rank \(0\).

Modular form 34914.2.a.o

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} + q^{11} + q^{12} - 4q^{13} + 2q^{14} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.