Properties

Label 303450.eo
Number of curves $4$
Conductor $303450$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.eo1 303450eo3 [1, 1, 1, -2698688, 1705259531] [2] 7077888  
303450.eo2 303450eo2 [1, 1, 1, -169938, 26169531] [2, 2] 3538944  
303450.eo3 303450eo1 [1, 1, 1, -25438, -996469] [2] 1769472 \(\Gamma_0(N)\)-optimal
303450.eo4 303450eo4 [1, 1, 1, 46812, 88593531] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 303450.eo have rank \(0\).

Complex multiplication

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

Modular form 303450.2.a.eo

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.