Properties

Label 301530.cs
Number of curves $4$
Conductor $301530$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("301530.cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301530.cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301530.cs1 301530cs4 [1, 0, 0, -1608171, -785092089] [2] 4325376  
301530.cs2 301530cs3 [1, 0, 0, -116391, -8141325] [2] 4325376  
301530.cs3 301530cs2 [1, 0, 0, -100521, -12270699] [2, 2] 2162688  
301530.cs4 301530cs1 [1, 0, 0, -5301, -253935] [2] 1081344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 301530.cs have rank \(1\).

Modular form 301530.2.a.cs

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - 2q^{13} - 4q^{14} - q^{15} + q^{16} + 2q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.