Properties

Label 334620ch
Number of curves 4
Conductor 334620
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("334620.ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 334620ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
334620.ch4 334620ch1 [0, 0, 0, -68952, -6826079] [2] 1866240 \(\Gamma_0(N)\)-optimal
334620.ch3 334620ch2 [0, 0, 0, -152607, 12966694] [2] 3732480  
334620.ch2 334620ch3 [0, 0, 0, -677352, 211863301] [2] 5598720  
334620.ch1 334620ch4 [0, 0, 0, -10799607, 13660291294] [2] 11197440  

Rank

sage: E.rank()
 

The elliptic curves in class 334620ch have rank \(0\).

Modular form 334620.2.a.ch

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} - q^{11} + 4q^{19} + O(q^{20}) \)

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.