Properties

Label 34650.ec
Number of curves 4
Conductor 34650
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("34650.ec1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 34650.ec

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34650.ec1 34650dp4 [1, -1, 1, -7422980, -7782276103] [2] 1179648  
34650.ec2 34650dp2 [1, -1, 1, -477230, -114168103] [2, 2] 589824  
34650.ec3 34650dp1 [1, -1, 1, -112730, 12677897] [2] 294912 \(\Gamma_0(N)\)-optimal
34650.ec4 34650dp3 [1, -1, 1, 636520, -568578103] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 34650.ec have rank \(1\).

Modular form 34650.2.a.ec

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.