Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("301530.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 301530.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
301530.cj1 301530cj3 [1, 1, 1, -328520, 72233207] [2] 3153920  
301530.cj2 301530cj2 [1, 1, 1, -26990, 348455] [2, 2] 1576960  
301530.cj3 301530cj1 [1, 1, 1, -16410, -811113] [2] 788480 \(\Gamma_0(N)\)-optimal
301530.cj4 301530cj4 [1, 1, 1, 105260, 2887655] [2] 3153920  

Rank

sage: E.rank()
 

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

Modular form 301530.2.a.cj

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.