Properties

Label 42350cq
Number of curves 4
Conductor 42350
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("42350.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42350cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42350.cx3 42350cq1 [1, 1, 1, -169463, -522599219] [2] 1658880 \(\Gamma_0(N)\)-optimal
42350.cx2 42350cq2 [1, 1, 1, -10817463, -13577047219] [2] 3317760  
42350.cx4 42350cq3 [1, 1, 1, 1524537, 14076292781] [2] 4976640  
42350.cx1 42350cq4 [1, 1, 1, -79000963, 262577985781] [2] 9953280  

Rank

sage: E.rank()
 

The elliptic curves in class 42350cq have rank \(0\).

Modular form 42350.2.a.cx

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

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.