Properties

Label 42350.cd
Number of curves $4$
Conductor $42350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("42350.cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42350.cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42350.cd1 42350bu4 [1, -1, 1, -809755, 280653497] [2] 491520  
42350.cd2 42350bu3 [1, -1, 1, -265255, -49071503] [2] 491520  
42350.cd3 42350bu2 [1, -1, 1, -53505, 3865997] [2, 2] 245760  
42350.cd4 42350bu1 [1, -1, 1, 6995, 356997] [2] 122880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42350.cd have rank \(1\).

Modular form 42350.2.a.cd

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.