Properties

Label 303450.k
Number of curves $4$
Conductor $303450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.k1 303450k3 [1, 1, 0, -36695925, 85545487125] [2] 28311552  
303450.k2 303450k4 [1, 1, 0, -4905925, -2212830875] [2] 28311552  
303450.k3 303450k2 [1, 1, 0, -2304925, 1321928125] [2, 2] 14155776  
303450.k4 303450k1 [1, 1, 0, 7075, 61888125] [2] 7077888 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.k have rank \(1\).

Complex multiplication

The elliptic curves in class 303450.k do not have complex multiplication.

Modular form 303450.2.a.k

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

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.