Properties

Label 301665.ca
Number of curves 4
Conductor 301665
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("301665.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301665.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301665.ca1 301665ca3 [1, 0, 1, -284938, 58516421] [2] 1966080  
301665.ca2 301665ca4 [1, 0, 1, -90588, -9762959] [2] 1966080  
301665.ca3 301665ca2 [1, 0, 1, -18763, 809681] [2, 2] 983040  
301665.ca4 301665ca1 [1, 0, 1, 2362, 74531] [2] 491520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301665.ca have rank \(1\).

Modular form 301665.2.a.ca

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - q^{7} - 3q^{8} + q^{9} + q^{10} - q^{12} - q^{14} + q^{15} - q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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 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.